We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅ there are differences. Our main result is a structure theory for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k.

A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of o-minimal expansions (...) of real closed fields. Here we further develop this analogy. We establish an o-minimal style cell decomposition for weakly o-minimal non-valuational expansions of ordered groups. For structures enjoying such a strong cell decomposition we construct a canonical o-minimal extension. Finally, we make attempts towards generalizing the o-minimal Euler characteristic to the class of sets definable in weakly o-minimal structures with the strong cell decomposition property. (shrink)

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VC-minimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full (...) VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density. (shrink)

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion of (...) R. Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

Social studies of interdisciplinary science investigate how scientific collaborations approach complex challenges that require multiple disciplinary perspectives. In order for collaborators to meet these complex challenges, interdisciplinary collaborations must develop and maintain integrative capacity, understood as the ability to anticipate and weigh tradeoffs in the employment of different disciplinary approaches. Here we provide an account of how one group of interdisciplinary fog scientists intentionally catalyzed integrative capacity. Through conversation, collaborators negotiated their commitments regarding the ontology of fog systems and (...) the methodologies appropriate to studying fog systems, thereby enhancing capabilities which we take to constitute integrative capacity. On the ontological front, collaborators negotiated their commitments by setting boundaries to and within the system, layering different subsystems, focusing on key intersections of these subsystems, and agreeing on goals that would direct further investigation. On the methodological front, collaborators sequenced various methods, anchored methods at different scales, validated one method with another, standardized the outputs of related methods, and coordinated methods to fit a common model. By observing the process and form of collaborator conversations, this case study demonstrates that social studies of science can bring into critical focus how interdisciplinary collaborators work toward an integrated conceptualization of study systems. (shrink)

O-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory for abstract-definable $C^{\infty (...) }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: [email protected]: https://doi.org/10.11606/T.45.2019.tde-28042019-181150. (shrink)

Fix a weakly minimal (i.e. superstable U-rank 1) structure M. Let M∗ be an expansion by constants for an elementary substructure, and let A be an arbitrary subset of the universe M. We show that all formulas in the expansion (M∗,A) are equivalent to bounded formulas, and so (M,A) is stable (or NIP) if and only if the M-induced structure AM on A is stable (or NIP). We then restrict to the case that M is a pure abelian group (...) with a weakly minimal theory, and AM is mutually algebraic (equivalently, weakly minimal with trivial forking). This setting encompasses most of the recent research on stable expansions of (Z,+). Using various characterizations of mutual algebraicity, we give new examples of stable structures of the form (M,A). Most notably, we show that if (G,+) is a weakly minimal additive subgroup of the algebraic numbers, A⊆G is enumerated by a homogeneous linear recurrence relation with algebraic coefficients, and no repeated root of the characteristic polynomial of A is a root of unity, then (G,+,B) is superstable for any B⊆A. (shrink)

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in (...) Belegradek et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

A totally ordered group G is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G{±∞}. Continuing work in Belegradek et al. 1115) and Point and Wagner 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group (...) of finite regular rank. Any pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property ); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions. (shrink)

Recently, psychological phenomena have been expanded to new domains, crisscrossing boundaries of organizational levels, with the emergence of areas such as social personality and ecosystem learning. In this contribution, we analyze the ascription of an individual-based concept (personality) to the social level. Although justified boundary crossings can boost new approaches and applications, the indiscriminate misuse of concepts refrains the growth of scientific areas. The concept of social personality is based mainly on the detection of repeated group differences across a (...) population, in a direct transposition of personality concepts from the individual to the social level. We show that this direct transposition is problematic for avowing the nonsensical ascription of personality even to simple electronic devices. To go beyond a metaphoric use of social personality, we apply the organizational approach to a review of social insect communication networks. Our conceptual analysis shows that socially self-organized systems, such as isolated ant trails and bee’s recruitment groups, are too simple to have social personality. The situation is more nuanced when measuring the collective choice between nest sites or foraging patches: some species show positive and negative feedbacks between two or more self-organized social structures so that these co-dependent structures are inter-related by second-order, social information systems, complying with a formal requirement for having social personality: the social closure of constraints. Other requirements include the decoupling between individual and social dynamics, and the self-regulation of collective decision processes. Social personality results to be sometimes a metaphorical transposition of a psychological concept to a social phenomenon. The application of this organizational approach to cases of learning ecosystems, or evolutionary learning, could help to ground theoretically the ascription of psychological properties to levels of analysis beyond the individual, up to meta-populations or ecological communities. (shrink)

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large (...) subsets of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X × Y, then for a large set of tuples $\langle \overline{a}_{1},\ldots,\overline{a}_{2^{k}}\rangle \in X^{2^{k}}$ , where k = dim(Y), the union of fibers $S_{\overline{a}_{1}}\cup \cdots \cup S_{\overline{a}_{2^{k}}}$ is large in Y. Finally, given a weakly o-minimal structure ������, we find various conditions equivalent to the fact that the topological dimension in ������ enjoys the addition property. (shrink)

Let M=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}=}$$\end{document} be a weakly o-minimal expansion of a dense linear order without endpoints. Some tame properties of sets and functions definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} which hold in o-minimal structures, are examined. One of them is the intermediate value property, say IVP. It is shown that strongly continuous definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} satisfy an extended (...) version of IVP. After introducing a weak version of definable connectedness in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document}, we prove that strong cells in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} are weakly definably connected, so every set definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} is a finite union of its weakly definably connected components, provided that M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} has the strong cell decomposition property. Then, we consider a local continuity property for definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} and conclude some results on cell decomposition regarding that property. Finally, we extend the notion of having no dense graph which was examined for definable functions in and related to uniform finiteness, definable completeness, and others. We show that every weakly o-minimal structure M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} having cell decomposition, satisfies NDG, i.e. every definable function in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} has no dense graph. (shrink)

We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document}. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document} if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.

Multifunctional agricultural systems seek to expand upon production-based benefits to enhance family wellbeing and animal health, reduce inputs, and improve environmental services such as biodiversity and water quality. However, in many countries a landscape-level conversion is uneven at best and stalled at worst. This is particularly true across the eastern rural landscape in the United States. We explore the role of social networks as drivers of system transformation within dairy production in the eastern United States, specifically rotational grazing as an (...) alternative management option. We hypothesize the importance of weak ties within farmer social networks as drivers of change. In Wisconsin, Pennsylvania, and New York, we conducted 53 interviews with confinement, low-intensity, and rotational grazing dairy producers as well as 35 interviews with associated network actors. Though confinement and grazier networks had similar proportions of strong and weak ties, confinement producers had more market-based weak ties, while graziers had more weak-ties to government agencies and other graziers in the region. These agency weak ties supported rotational graziers through information exchange and cost sharing, both crucial to farmers’ transitions from confinement-based production to grazing systems. While weak ties were integral to initial innovation, farmers did not maintain these relationships beyond their transition to grazing. Of equal importance, grazier weak-tie networks did not include environmental organizations, suggesting unrealized potential for more diverse networks based on environmental services. By understanding the drivers, we can identify barriers to expanding weak tie networks and emergent properties in order to create institutions and policies necessary for change. (shrink)

The experience of the use of applied containerized biomedical software tools in cloud environment is summarized. The reproducibility of scientific computing in relation with modern technologies of scientific calculations is discussed. The main approaches to biomedical data preprocessing and integration in the framework of the intelligent analytical system are described. At the conditions of pandemic, the success of health care system depends significantly on the regular implementation of effective research tools and population monitoring. The earlier the risks of disease can (...) be identified, the more effective process of preventive measures or treatments can be. This publication is about the creation of a prototype for such a tool within the project «Development of methods, algorithms and intelligent analytical system for processing and analysis of heterogeneous clinical and biomedical data to improve the diagnosis of complex diseases», implementted by the V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, together with the United Institute of Informatics Problems, National Academy of Sciences of Belarus. The insurers, entering the market, can insure mostly low risks by facilitating more frequent changes of insurers by consumers and mixing the overall health insurance market. Socio-demographic variables can be risk adjusters. Since age and gender have a relatively small explanatory power, other socio-demographic variables were studied – marital status, retirement status, disability status, educational level, income level. Because insurers have an interest in beneficial diagnoses for their policyholders, they are also interested in the ability to interpret relevant information – upcoding: insurers can encourage their policyholders to consult with doctors more often to select as many diagnoses as possible. Many countries and health care systems use diagnostic information to determine the reimbursement to a service provider, revealing the necessary data. For processing and analysis of these data, software implementations of construction for classifiers, allocation of informative features, processing of heterogeneous medical and biological variables for carrying out scientific research in the field of clinical medicine are developed. The experience of the use of applied containerized biomedical software tools in cloud environment is summarized. The reproducibility of scientific computing in relation with modern technologies of scientific calculations is discussed. Particularly, attention is paid to containerization of biomedical applications, this permits to get reproducibility of the conditions in which the calculations took place, technologies of software pipelining of calculations, that allows to organize flow calculations, and technologies for parameterization of software environment, that allows to reproduce, if necessary, an identical computing environment. The main approaches to biomedical data preprocessing and integration in the framework of the intelligent analytical system are described. The experience of using the developed linear classifier, gained during its testing on artificial and real data, allows us to conclude about several advantages provided by the containerized form of the created application: it permits to provide access to real data located in cloud environment; it is possible to perform calculations to solve research problems on cloud resources both with the help of developed tools and with the help of cloud services; such a form of research organization makes numerical experiments reproducible, i.e. any other researcher can compare the results of their developments on specific data that have already been studied by others, in order to verify the conclusions and technical feasibility of new results; there exists a universal opportunity to use the developed tools on technical devices of various classes from a personal computer to powerful cluster. (shrink)

Generally, public opinion is measured via polls or survey instruments, with a majority of responses in a particular direction taken to indicate the presence of a given ‘public opinion’. However, discursive psychological and related scholarship has shown that the ontological status of both individual opinion and public opinion is highly suspect. In the first part of this article I draw on this body of work to demonstrate that there is currently no meaningful theoretical foundation for the construct of public opinion (...) as it is typically measured in surveys, polls, or focus groups. I then argue that there is a particular sense in which the construct of public opinion does make sense. In deliberative democratic forums participants engage in dialogue with the aim of coming to collective positions on particular issues. Here I draw on examples of deliberative democratic forums conducted on the social and ethical implications of science and technology. Conversation between participants in deliberative democratic forums is ideally characterized by individuals becoming informed about the issues being discussed, respectful interactions between participants, individuals being open to changing their positions, and a convergence towards collective positions in the interest of formulating civic solutions. The end-product of deliberation on a given issue might thus be termed a deliberative public opinion. ‘Deliberative public opinion’ is neither a cognitive nor an aggregate construct, but rather a socio-historical product. Criteria for its legitimacy rely on the inclusiveness of diversity of perspectives and the degree to which collective positions are defensible to a larger society. (shrink)

The objectives of this study were to develop a high-density chromosome bin map of homoeologous group 7 in hexaploid wheat, to identify gene distribution in these chromosomes, and to perform comparative studies of wheat with rice and barley. We mapped 2148 loci from 919 EST clones onto group 7 chromosomes of wheat. In the majority of cases the numbers of loci were significantly lower in the centromeric regions and tended to increase in the distal regions. The level of (...) duplicated loci in this group was 24% with most of these loci being localized toward the distal regions. One hundred nineteen EST probes that hybridized to three fragments and mapped to the three group 7 chromosomes were designated landmark probes and were used to construct a consensus homoeologous group 7 map. An additional 49 probes that mapped to 7AS, 7DS, and the ancestral translocated segment involving 7BS also were designated landmarks. Landmark probe orders and comparative maps of wheat, rice, and barley were produced on the basis of corresponding rice BAC/PAC and genetic markers that mapped on chromosomes 6 and 8 of rice. Identification of landmark ESTs and development of consensus maps may provide a framework of conserved coding regions predating the evolution of wheat genomes. (shrink)

The focus of this study was to analyze the content, distribution, and comparative genome relationships of 996 chromosome bin-mapped expressed sequence tags accounting for 2266 restriction fragments on the homoeologous group 3 chromosomes of hexaploid wheat. Of these loci, 634, 884, and 748 were mapped on chromosomes 3A, 3B, and 3D, respectively. The individual chromosome bin maps revealed bins with a high density of mapped ESTs in the distal region and bins of low density in the proximal region of (...) the chromosome arms, with the exception of 3DS and 3DL. These distributions were more localized on the higher-resolution group 3 consensus map with intermediate regions of high-mapped-EST density on both chromosome arms. Gene ontology classification of mapped ESTs was not significantly different for homoeologous group 3 chromosomes compared to the other groups. A combined analysis of the individual bin maps using 537 of the mapped ESTs revealed rearrangements between the group 3 chromosomes. Approximately 232 of the consensus mapped ESTs matched sequences on rice chromosome 1 and revealed large- and small-scale differences in gene order. Of the group 3 mapped EST unigenes ∼21 and 32% matched the Arabidopsis coding regions and proteins, respectively, but no chromosome-level gene order conservation was detected. (shrink)

To localize wheat ESTs on chromosomes, 882 homoeologous group 6-specific ESTs were identified by physically mapping 7965 singletons from 37 cDNA libraries on 146 chromosome, arm, and sub-arm aneuploid and deletion stocks. The 882 ESTs were physically mapped to 25 regions flanked by 23 deletion breakpoints. Of the 5154 restriction fragments detected by 882 ESTs, 2043 were localized to group 6 chromosomes and 806 were mapped on other chromosome groups. The number of loci mapped was greatest on chromosome (...) 6B and least on 6D. The 264 ESTs that detected orthologous loci on all three homoeologs using one restriction enzyme were used to construct a consensus physical map. The physical distribution of ESTs was uneven on chromosomes with a tendency toward higher densities in the distal halves of chromosome arms. About 43% of the wheat group 6 ESTs identified rice homologs upon comparisons of genome sequences. Fifty-eight percent of these ESTs were present on rice chromosome 2 and the remaining were on other rice chromosomes. Even within the group 6 bins, rice chromosomal blocks identified by 1-6 wheat ESTs were homologous to up to 11 rice chromosomes. These rice-block contigs were used to resolve the order of wheat ESTs within each bin. (shrink)

The relation between least and diagonal fixed points is a well known and completely studied question for a large class of partially ordered models of the lambda calculus and combinatory logic. Here we consider this question in the context of algebraic recursion theory, whose close connection with combinatory logic recently become apparent. We find a comparatively simple and rather weak general condition which suffices to prove the equality of least fixed points with canonical (corresponding to those produced by the (...) Curry combinator in lambda calculus) diagonal fixed points in a class of partially ordered algebras which covers both combinatory spaces of Skordev and operative spaces of Ivanov. Especially, this yields an essential improvement of the axiomatization of recursion theory via combinatory spaces. (shrink)

The precarious rights of senior citizens, especially those who are highly educated and who are expected to counsel and guide the younger generations, has stimulated the creation internationally of advocacy associations and opinion leader groups. The strength of these groups, however, varies from country to country. In some countries, they are supported and are the focus of intense interest; in others, they are practically ignored. For this is reason we believe that the creation of a network of all these associations (...) is essential. The proposed network would act as a support for the already-existing policies of the United Nations’ High Commission for Human Rights, of independent experts, and of the Global Alliance for the Rights of Older People. All three have long ago recommended the creation of a recognized instrument for uniting presently scattered efforts. The proposed network, therefore, will seek to promote the international exchange of relevant expertise, and it will reinforce the commitments and actions that single countries are currently taking to meet these objectives. For example, informative public events can be organised to promote particular support initiatives and to provide an opportunity for new members of the network to be presented. The network will promote health for senior citizens, disease prevention, senior mobility, safe free time for seniors, alimentary education, protection against new risks and dangers, as well as equity in the services necessary for seniors to adopt new information and communication technologies. In the case of retired academic members, the network will promote equality with respect to continuing use of digital technologies (particularly email), continuing access to research libraries, and the guaranteed ability for seniors to fund their own research programs and to deliver free seminars. (shrink)

Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inp-minimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitely many continuous locally monotonic functions (Theorem 3.2).

In ‘Rethinking Disease’, Powell and Scarffe1 propose what in effect is a modification of Jerome Wakefield’s2 3 harmful dysfunction analysis of medical disorder. The HDA maintains that ‘disorder’ is a hybrid factual and value concept requiring that a biological dysfunction, understood as a failure of some feature to perform a naturally selected function, causes harm to the individual as evaluated by social values. Powell and Scarffe accept both the HDA’s evolutionary biological function component and its incorporation of a value component. (...) Their proposed ‘new twist’ is to revise the value component: ‘Our proposed definition of disease is as follows: a biomedical state is a disease only if it implicates a biological dysfunction that is, or would be, properly disvalued’. So, they propose that a disorder is a ‘properly disvalued dysfunction’ rather than a ‘harmful dysfunction’, an approach they term ‘thickly normative’ in contrast to the thin normative approach of the HDA. There has been a surge of interest recently in better understanding the ‘harm’ component of the HDA. Powell and Scarffe’s analysis is a helpful contribution to this discussion. We focus here exclusively on their proposal regarding the analysis of the concept of disorder and ignore many important related issues that the authors address, ranging from prioritising resource allocation between disorders and non-disorders to whether the concept of disorder should be replaced by a generic welfarist concept. The resolution of these additional issues depends on first understanding ‘disorder’. The authors’ proposed changes to the HDA also deserve evaluation because the HDA, which has been endorsed by leading nosologists,4 plays an influential role in nosological debate across categories of disorder ranging, for example, from sexual paraphilias5 to psychopathy.6 A basic problem is that Powell and Scarffe misinterpret …. (shrink)

Accumulating evidence for the unique social, behavioral, and physical health benefits of positive emotion and related well-being constructs has led to the development and testing of positive psychological interventions to increase emotional well-being and enhance health promotion and disease prevention. PPIs are specifically aimed at improving emotional well-being and consist of practices such as gratitude, savoring, and acts of kindness. The purpose of this narrative review was to examine the literature on PPIs with a particular focus on positive emotion outcomes. (...) We evaluated the evidence on the effects of PPIs on positive emotion specifically, and discussed the range of evidence regarding the relative responsiveness of emotion measures to PPIs in order to gain a better understanding of the specific emotional pathways through which PPIs influence psychological and physical well-being. We conclude with recommendations for best evaluating effects of PPIs on positive emotion outcomes. (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

Here we study properties of weakly circularly minimal cyclically ordered groups. The main result of the paper is that any weakly circularly minimal cyclically ordered group is abelian.

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

The Inforare project aims to set up a system for the sharing of clinical and familial data, in order to study how genes are related to the severity of sickle cell disease. While the computerisation of clinical records represents a valuable research goal, an ethical framework is necessary to guarantee patients' protection and their rights in this developing field. Issues relating to patient information during the Inforare study were analysed by the steering committee. Several major concerns were discussed by the (...) committee and formalised in the patients' information letter: educating patients to aid the recruitment of family members, rules of confidentiality and the disclosure of aggregate, individual and unexpected research results. This paper presents the main issues addressed. (shrink)

Objective: To evaluate feasibility of the guidelines of the Groupe Francophone de Réanimation et Urgence Pédiatriques for limitation of treatments in the paediatric intensive care unit .Design: A 2-year prospective survey.Setting: A 12-bed PICU at the Hôpital Jeanne de Flandre, Lille, France.Patients: Were included when limitation of treatments was expected.Results: Of 967 children admitted, 55 were included with a 2-day median delay. They were younger than others , had a higher paediatric risk of mortality score , and a higher paediatric (...) overall performance category score at admission ; all p<0.002. 34 children died. A limitation decision was made without meeting for 7 children who died: 6 received do-not-resuscitate orders and 1 received withholding decision. Decision-making meetings were organised for 31 children, and the following decisions were made: 12 DNROs , 4 withholding , with 14 withdrawing and 1 continuing treatment . After limitation, 21 children died and 10 survived . 13 procedures were interrupted because of death and 11 because of clinical improvement . Parents’ opinions were obtained after 4 family conferences , 3 days after inclusion. The first meeting was planned for 6 days after inclusion and held on the 7th day after inclusion; 80% of parents were immediately informed of the decision, which was implemented after half a day.Conclusions: GFRUPs procedure was applicable in most cases. The main difficulties were anticipating the correct date for the meeting and involving nurses in the procedure. Children for whom the procedure was interrupted because of clinical improvement and who survived in poor condition without a formal decision pointed out the need for medical criteria for questioning, which should systematically lead to a formal decision-making process. (shrink)

The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature $\{ . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the (...) Exchange Principle for algebraic closure in a weakly o-minimal structure. (shrink)

The Oxford Handbook of Philosophical Theology attempts both to familiarize readers with the directions in which the scholarship of this discipline has gone and to pursue the discussion into hitherto under-examined areas. Philosophical theology is aimed primarily at theoretical understanding of the nature and attributes of God and of God's relationship to the world and its inhabitants. During the twentieth century, much of the philosophical community (both in the Anglo-American analytic tradition and in Continental circles) had grave doubts about our (...) ability to attain any such understanding. In recent years the analytic tradition in particular has moved beyond the biases that placed obstacles in the way of the pursuing questions located at the interface of philosophy and religion. Written by some of the leading scholars in the field, the articles in the book are grouped into five sections. In the first section, articles focus on the authority of scripture and tradition, on the nature and mechanisms of divine revelation, on the relation between religion and science, and on theology and mystery. The next section focuses on philosophical problems connected with the central divine attributes: aseity, omnipotence, omniscience, and the like. In the third section, articles explore theories of divine action and divine providence, questions about petitionary prayer, problems about divine authority and God's relationship to morality and moral standards, and various formulations of and responses to the problem of evil. The fourth section examines philosophical problems that arise in connection with such central Christian doctrines as the trinity, the incarnation, the atonement, original sin, resurrection, and the Eucharist. Finally, the fifth section introduces readers to current work in Jewish, Islamic, and Chinese philosophical theology. (shrink)

We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.

An issue that affects the academic engagement, performance, health and wellbeing of university undergraduates is bullying. Substantial literature has examined the predictors of bullying perpetration, but there is little research on the contributions of internet-related factors and the propensity to take risks in bullying. We examined the roles of IGD, risk-taking behavior, and internet addiction in social bullying. Four instruments were used for data collection, namely: Young Adult Social Behavior Scale, the Internet Gaming Disorder Scale, Domain-Specific Risk-Taking Scale, and the (...) Internet Addiction Test Scale. Participants were 552 undergraduate students from the University of Nigeria, Nsukka consisting of 143 males and 409 females. Results of regression analysis showed that gaming disorder and risk-taking behavior had positive associations with social bullying. Thus, the more people grow addicted to internet gaming and takes more risks, the more they are likely to become bullies. Internet addiction had no significant association with social bullying. Efforts should be made to minimize the rate of dysfunctional internet use, GD and risk-taking behaviors of undergraduates in order to curtail bullying perpetration. (shrink)

We continue exploring analogues of o-minimality and weak o-minimality for circularly ordered sets. The main result is a description of ℵ0-categorical 1-transitive non-primitive weakly circularly minimal structures of convexity rank 1 up to binarity.

During his time as Archbishop of Canterbury, Rowan Williams addressed the relations between Christianity and science at some length. While many contemporary theologians have explored the natural sciences in detail and have deployed scientific ideas and concepts in their theological work, Williams's writings suggest that theology has little need for natural scientific knowledge. For Williams, the created order's relationship to God renders the content of scientific theories about how finite causes are materially constituted and interact of little theological importance. At (...) the same time, Williams is convinced that theological and scientific work must each remain within their proper bounds, a position that can best succeed in practice when participants in each discipline are aware of how both disciplines approach their subject matter. Although Williams's view challenges those who would insist that theology requires anything more than minimal engagement with the sciences, the ability to clearly demarcate and preserve the boundaries between scientific and theological work nevertheless requires of the theologian the kind of understanding of scientific methods and theories that Williams himself demonstrates. (shrink)

Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.

0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...) classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry. (shrink)

Quons are particles characterized by the parameter q, which permits smooth interpolation between Bose and Fermi statistics; q = 1 gives bosons, q = -1 gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form ffb, where f is fermion-like and b is boson-like. We show that q f 2 = qb. In particular, we relate the bound on qγ for photons to the bound on (...) qe for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to a high precision. (shrink)

Abortion is permitted in many jurisdictions after the age at which an infant is viable on the basis of intensive neonatal care techniques. Does this cause special concerns for those involved in perinatal care and termination of pregnancy services or is the overlap mainly an abstract issue fretted over by ethicists and academics? In order to explore this question, a group of clinicians involved in this area of care were interviewed and their interviews analysed using qualitative measures. The clinicians (...) concerned were exercised by the ethical issues and had various ways of resolving them which tended to reflect a gradualist, multifaceted and, to some extent, particularist approach to ethical decision-making in relation to the edges of human life. The ways in which those strands of ethical thought are instanced in the interview material are reported and discussed. (shrink)

In the last years of its history, the Ukrainian ethnic group faced numerous external and internal challenges, which, to a large extent, were the result of its previous genesis and profound transformations in public consciousness. At the same time, one of the central stereotypes of the domestic political and legal mentality is the idea of truth and justice as a basic social ideal and the basis of the legal order. Analysis of research and publications. The problem of mentality and (...) the formation of behavioral stereotypes has been of interest to domestic and foreign scientists for a long time. The concept of «mentality» is most widespread in the writings of the French historical school «Annals». The scientific work of M. Blok, F. Braudel, M. Vovel, J. Le Hoff, J. Lefebvre, L. Fevre, R. Mandr and other scientists reveals the content of mentality and its structures, as well as the peculiarities of their influence on everyday life and activities of individuals who lived in different historical eras. The purpose and objectives of the article. In this article, the authors aim to analyze the idea of truth-justice as a tool for transforming the legal mentality of the Ukrainian ethnic group and to show its influence on the content of its behavioral stereotypes. Research methodology. The methodology of this research has a complex nature and is based on a socio-philosophical and philosophical-legal analysis of the behavioral guidelines of Ukrainians in the field of legal understanding. The results. The social ideology, developed on the basis of ancient social ideas and stereotypes of the national legal mentality, should become a tool for correcting such destructive phenomena in the state-building discourse as legal nihilism, anarchism, civic passivity, corruption, nepotism, etc. At the same time, the concepts of truth-justice, will-freedom and fraternity-equality are key in Ukrainian legal culture. Discussion. The interpretation of this idea in scientific opinion is not unambiguous. This idea clearly manifests itself in the context of the opposition between Truth and Evil in the national culture. Truth is inseparable from human existence and daily activities. The idea of truth is closely related to the idea of justice, which, according to many researchers, is a later, more rational and clearly defined phenomenon derived from truth. Justice as a socio-philosophical phenomenon is intended to act as a kind of moral measure of relations between individuals in society. It is considered as an authoritative criterion for establishing the correspondence between the nature of human activity and its assessment by the social community. Conclusions. Destructive behavioral stereotypes of the Ukrainian ethnic group that were formed, among other things, under the influence of factors of stressogenesis can be corrected with the help of the legal ideology of state building, which should be based on the content of the idea of truth and justice. The developed ideology should be based on the most stable constructive guidelines of the national legal mentality, organically complementing and ideologically justifying them. (shrink)

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that include (...) compact spaces. However, we offer a negative result that continuity may not be reached under such hypotheses. (shrink)

Given a weakly o-minimal theory T, the T-height of an element of a model of T is defined as a means of classifying the order of magnitude of the element. If T satisfies some easily met technical conditions, then this classification is coarse enough for a Wilkie-type inequality: given a set of elements of a model of T, each of which has a different T-height, the cardinality of this set is at most 1 plus the minimum cardinality of a set (...) that generates the structure. (shrink)

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.

According to Hume, humans, unlike other group-living animals, cannot accommodate their natural sexual appetite naturally; this is a Rawlsian 'circumstance of justice'. Humans have to formulate conventions or artifices to govern their reproductive relations in order to maintain their group or social life. Hume implicitly addresses this issue in his discussion of chastity. The paper explicates his argument. This argument, and its underlying philosophical anthropology, is seen to embody a distinctive approach to a striking feature of the human (...) condition -- sexual relations are universal but not uniform. (shrink)

Le regard théologique sur la question du mal a progressé en Occident grâce à la lecture des Noms divins de Denys, et à l'analyse scientifique de Thomas d'Aquin. Il est cependant intéressant de souligner le nouvel ordre et les rectifications que Thomas d'Aquin apporte à la pensée de Denys dont il est tributaire. Imprégné de la philosophie néoplatonicienne, Denys apparaît dans son ouvrage comme faisant une théologie de l'amour et du Bien. Le Bien y est non seulement objet d'amour, mais (...) il appelle un ordre et une vie. Le mal ne peut être situé que par rapport à l'opération vitale défaillante. Par rapport à Denys, Thomas d'Aquin opère une inversion de pensée. Son apport propre est de dépasser les deux positions de Denys selon qui le mal n'a pas de cause propre, le Bien étant fin de tous les maux. Le mal, qui reste accidentel pour Thomas, est aussi le fruit d'une relation déséquilibrée. Conséquence du péché en tant que mal de peine, tout est-il résolu par là quant au problème du mal ? Par delà saint Thomas, n'y a-t-il pas demande aujourd'hui d'un regard lucide sur la relation réciproque, c'est-à-dire le rôle inhibiteur que joue souvent l'excès de souffrance dans la relation à Dieu ? Theology's attitude to the question of evil has progressed in the West, thanks to the study of Dionysius' Divine Names and the scientific analysis of Thomas Aquinas. It is, nevertheless, interesting to underline the new method and rectifications that Thomas Aquinas brings to the thought of Dionysius, upon which he depends. Dionysius, impregnated with neo-Platonic philosophy, seems to elaborate a theology of love and the Good in his work. He sees the Good as not only the object of love, but calling for an order and a life. Evil can only be situated in terms of a vital operation that is faulted. In comparison with Dionysius, Thomas Aquinas operates an inversion of thought. His own contribution is to go beyond the two positions of Dionysius, according to whom evil does not have its own cause, the Good being the end of all evils. Evil, which remains accidental for Thomas, is also the fruit of an unbalanced relation. The consequence of sin in terms of the evil of pain does this resolve all the problems concerning evil ? Beyond St. Thomas, isn’t there a need today of a clear perspective about reciprocal relation, the inhibiting role that the excess of suffering often plays in the relation to God ? (shrink)

La réception tardive de l'oeuvre de Ernst Troeltsch en France nous a privés d'une analyse du christianisme originale et féconde. Elle nuance et enrichit ce que nous savons, au travers de la réflexion wébérienne notamment, des relations de la religion chrétienne à la modernité. Contre les interprétations usuelles qui datent l'émergence de cette dernière de la Renaissance et de la Réforme, Troeltsch insiste sur la centralité des Lumières comme marquant la fin de la civilisation ecclésiastique ; c'es l'évanouissement de la (...) référence structurante à l'ordre divin qui inau­gure selon lui l'entrée dans le monde moderne. Sur la base de ce constat, il s'agit pour Troeltsch de trouver une définition du christianisme qui soit en adéquation avec les conditions de l'existence moderne. Dans son ouvrage datant de 1912, « Les doctrines sociales des Églises et groupes chrétiens », il examine les types « Église », « secte » et « mystique » pré­sents depuis les origines évangéliques, circonscrivant trois modes socio­logiques et éthiques qu'il confronte à la modernité. Aucun n'est seul adéquat. Pour durer, le christianisme devra, selon Troeltsch, renoncer à la réalisation d'un programme éthique d'essence religieuse au sein du monde et accepter le cantonnement de la foi dans l'intimité des cons­ciences, tout en s'articulant à des réalités socio-culturelles à l'échelle de tous dont les formes et les transformations internes sont toujours à repenser.The delayed reception of the work of Ernst Troeltsch in France deprived us of an analysis of an original and fertile Christianity. It nuances and enriches what we know, especially through a Weberian reflection, about the relations of the Christian religion and modernity. Against the customary interpretations that date the emergence of the latter from the Renaissance and the Reformation, Troeltsch insists on the centrality of the Enlightenment as marking the end of an ecclesiastical civilization. It is the disappearance of the structuring reference to the divine order that inaugurated, according to him, the entrance to the modern world. On the basis of this observation, Troeltsch is interested in finding a definition of Christianity that would be in harmony with the conditions of modern existence. In his work dating from 1912, "The social doctrines of the Churches and Christian groups ", he examines the categories "Church", "sect", and "mystic" that were present evangelical times, circumscribing three sociological and ethical modes, which he confronts with modernity. No single one is adequate. In order to endure, Christian­ity should, according to Troeltsch, renounce the attempt to set up an ethical program of a religious essence in the heart of the world and accept the establishment of a faith in the intimacy of consciences, all the while adapting its« to socia-cultural realities applicable to everyone, of which the forms and internal transformations are always to be re-thought. (shrink)

Discrete weakly o-minimal structures, although not so stimulating as their dense counterparts, do exhibit a certain wealth of examples and pathologies. For instance they lack prime models and monotonicity for definable functions, and are not preserved by elementary equivalence. First we exhibit these features. Then we consider a countable theory of weakly o-minimal structures with infinite definable discrete subsets and we study the Boolean algebra of definable sets of its countable models.

George Berkeley maintains both anti-abstractionism (that abstract ideas are impossible) and idealism (that physical objects and their qualities are mind-dependent). Some scholars (including Atherton, Bolton, and Pappas) have argued, in different ways, that Berkeley uses anti-abstractionism as a premise in a simple argument for idealism. In this paper, I argue that the relation between anti-abstractionism and idealism in Berkeley's metaphysics is more complex than these scholars acknowledge. Berkeley distinguishes between two kinds of abstraction, singling abstraction and generalizing abstraction. He then (...) rests his case for idealism, not on the denial of the possibility of generalizing abstraction, but rather on the denial of the possibility of singling abstraction. Moreover, Berkeley's argument does not rest on a blanket rejection of all forms of singling abstraction. Rather, the fundamental anti-abstractionist assumption, for his purposes, is the claim that primary qualities cannot be mentally singled out from secondary qualities. Crucially, the claim that the existence of physical objects cannot be mentally singled out from their being perceived is not a premise in, but rather a consequence of, Berkeley's argument for idealism. Berkeley's argument therefore avoids circularity inasmuch as it appeals to the impossibility of singly abstracting one idea in order to establish the impossibility of singly abstracting another. (shrink)

We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within (...) expansions of Boolean lattices, every weakly o-minimal theory is p-ω-categorical. (shrink)

Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one (...) complete, MP(S) implies the usual Markov's Principle MP. An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implies MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP. These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Godel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article. (shrink)