We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.

The main results in the paper are the following. Theorem A. Suppose that T is superstable and M ⊂ N are distinct models of T eq . Then there is a c ϵ N⧹M such that t is regular. For M ⊂ N two models we say that M ⊂ na N if for all a ϵ M and θ such that θ ≠ θ , there is a b ∈ θ ⧹ acl . Theorem B Suppose that T (...) is superstable , M ⊂ na N are models of T eq , and p is a regular type non-orthogonal to t . Then there is a c ϵ N such that t is regular and non-orthogonal to p. Furthermore, there is a formula θ ∈ t such that a ∈ θ and t ⊥ ̷ p ⇒ t is regular. We used these results to obtain ‘good’ tree decompositions of models in superstable theories with NDOP. See Definition 5.1 for the undefined terms. Theorem C Suppose that T is superstable with NDOP and M ⊨ T eq . Then every ⊂ na - decomposition inside M extends to a ⊂ na -decomposition of M. Furthermore, if 〈N η , a η : η ∈ I〉 is any ⊂ na -decomposition of M, then M is minimal over ∪N η and for all η ∈ I. M is dominated by ∪N η over N η . Using some stable group theory we show that when Th is superstable with NDOP and 〈 N η : η ∈ I 〉 is a tree decomposition of M, then M is constructible over ∪ n η with respect to a very strong isolation relation. (shrink)

We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ (...) of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11]. (shrink)

Let $M$ be a saturated model of a superstable theory and let $G = \operatorname{Aut}(M)$. We study subgroups $H$ of $G$ which contain $G_{(A)}, A$ the algebraic closure of a finite set, generalizing results of Lascar [L] as well as giving an alternative characterization of the simple superstable theories of [P]. We also make some observations about good, locally modular regular types $p$ in the context of $p$-simple types.

Former discussions of biological generalizations have focused on the question of whether there are universal laws of biology. These discussions typically analyzed generalizations out of their investigative and explanatory contexts and concluded that whatever biological generalizations are, they are not universal laws. The aim of this paper is to explain what biological generalizations are by shifting attention towards the contexts in which they are drawn. I argue that within the context of any particular biological explanation or investigation, biologists employ two (...) types of generations. One type identifies causal regularities exhibited by particular kinds of biological entities. The other type identifies how these entities are distributed in the biological world. (shrink)

Physical activity, specifically exercising, has been suggested to improve body image, mental health, and well-being. With respect to body image, previous findings highlight a general benefit of exercise. This study investigates whether the relationship between exercising and body image varies with the type of exercise that individuals preferentially and regularly engage in. In addition, physical efficacy was explored as a potential psychological mediator between type of exercise and body image. Using a cross-sectional design, healthy regular exercise practitioners of yoga, (...) ballroom dance, team sports, or individual sports as well as healthy adults reporting no regular exercising were surveyed. Body image and its different facets were assessed by a set of standardized self-report questionnaires, covering perceptual, cognitive, and affective body image dimensions particularly related to negative body image. In addition, participants were questioned with regard to mental health. Participants were 270 healthy adults. Descriptive statistics, measures of variance, and multiple linear regression analysis with orthogonal contrasts were performed to investigate differences between the different exercise and non-exercise groups in the variables of interest. In line with the hypotheses and previous findings, the statistic comparisons revealed that body dissatisfaction was most pronounced in the non-exercise group compared to all exercise groups [contrast: no exercise versus exercise ]. Physical efficacy, as assessed with a standardized questionnaire, mediated the difference between type of exercise and body image including perceptual, cognitive, and affective body image dimensions. The findings shed light on so far less systematically investigated questions regarding the relationship between types of exercise, like yoga and ballroom dance, and body image. The results underscore the relevance of considering possible influencing factors in exercise research, such as the perception of one’s physical efficacy as a mediator of this relationship. (shrink)

We present an alternative solution to the problem of inductive generation of covers in formal topology by using a restricted form of type universes. These universes are at the same time constructive analogues of regular cardinals and sets of infinitary formulae. The technique of regular universes is also used to construct canonical positivity predicates for inductively generated covers.

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenPhas unbounded orbit (...) under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable. (shrink)

In reply to certain cosmological arguments for theism, critics regularly argue that the causal principle ex nihilo nihil fit may be false. Various theistic counter-replies to this challenge have emerged. One type of strategy is to double down on ex nihilo nihil fit. Another, very different strategy of counter-reply is to grant for the sake of argument that the principle is false, while maintaining that sound cosmological arguments can be formulated even with this concession in place. Notably, one can employ (...) a weaker opening premise formulated in modal terms, proceeding for instance from the proposition that for any contingent object coming into existence it is at least possible that it have a cause. My aim here is to try out a related strategy for weakening the relevant opening premise. Granting that it is possible for a contingent object to come into existence out of nothing without a cause, I proceed from the extremely modest claim that the obtaining of exceptionless longstanding contingent regularities demands an explanation. As such, the contingent regularity that empirically accessible macro-level contingent objects do not pop into existence causelessly demands explanation. And as it turns out, that explanation will have to be in terms of an object or objects possessed of at least some of the traditional divine attributes. (shrink)

This article deals with the control of chaos on the convective motion in a ferrofluid filled in a rotating porous medium and under the helical force effect. We performed a truncated expansion of Galerkin and found the Lorenz-type model which described the system. The dynamical system is characterized using appropriate and subsequent criteria. We noticed that the system presents regular and chaotic behaviors according to the parameters at present. A considerable reduction of the chaotic domain is noticed with the (...) increase of the intensity of the helical force and of the Darcy number, thus making it possible to delay the heat transfer in the system. The increase in the viscosity ratio and the Taylor number widen the chaotic domain leading to an acceleration of the heat transfer in the system. (shrink)

This is a continuation of [3]. We deal with algebras of type : T ! N. Assume that V is a variety of type . Let p = x be a strongly nonregular identity satised in V , i.e. x; y are variables of p and x =6 y . For a variety K 2 L; E; R; S or RS denotes the set of all, regular, symmetric or regular and symmetric identities satised in K, respectively.

J. P lonka at WSP in Opole, in 1980 and 1981. We shall consider algebras o type : T ! N; E, R, S denote the set of all identities of type and the set of all regular identities of type , respectively . If is a set of identities of type , then E() denotes the set of all identities which can be proved from ; R() = \ R, S() = \ S. denotes the variety generated by (...) . Similarly, for a given variety V of algebras of type we shall consider varieties R and S dened by the set R of all regular identities satised in V and the set S of all symmetric identities satised in V , respectively. (shrink)

The institution of slavery has served to perform different functions in different societies. The distinction between ‘closed’ and ‘open’ slavery can be a useful one: in some societies slavery is a mechanism for the permanent exclusion of certain individuals from political and economic privileges, while in others it has served precisely to facilitate the integration of outsiders into the community. ‘The African slave, brought by a foray to the tribe, enjoys, from the beginning, the privileges and name of a child, (...) and looks upon his master and mistress in every respect as his new parents… by care and diligence, he may soon become a master himself, and even more rich and powerful than he who led him captive.’ The model of an ‘open’ slavery implies that service as a slave is not a state to which a person is permanently, let alone ‘naturally’, assigned, but more akin to an age-grade. A parallel might be domestic or agricultural service as it was practised in much of Europe until this century — a period spent serving in another household after childhood and prior to marriage. A Roman slave, on formal manumission, joined the community of citizens. To what extent ought we therefore to succumb to the temptation to see slavery at Rome — in contrast to the Greek world — in terms of the ideal type of a ‘process of integration’? In a noted article on ‘Die Freilassung von Sklaven und die Struktur der Sklaverei in der römischen Kaiserzeit’ , G. Alföldi argued that in the Roman Empire slavery was an ‘Übergangszustand’ , a transitional state which ultimately gave most slaves a recognised if not a fully equal place as members of the Roman citizen community. (shrink)

c causes e iff i. c is spatiotemporally contiguous to e; ii. e succeeds c in time; and iii. all events of type C (i.e., events that are like c) are regularly followed by (or are constantly conjoined with) events of type E (i.e., events like e).

The paper deals with of one aspect of “The Laws”: the rules proposed on partying, drinking and the type of music and dance presided over by Dionysus. The Athenian tries to combine: a) the need for education to form law-abiding citizens capable of defending the city; b) the need to control the disturbing effects of drinking and debauchery on music and dance; and c) the desire to maintain the Athenian tradition they were proud of: the conciliation of military excellence and (...) the fun produced by drinking, music and dance. (shrink)

The paper deals with of one aspect of “The Laws”: the rules proposed on partying, drinking and the type of music and dance presided over by Dionysus. The Athenian tries to combine: a) the need for education to form law-abiding citizens capable of defending the city; b) the need to control the disturbing effects of drinking and debauchery on music and dance; and c) the desire to maintain the Athenian tradition they were proud of: the conciliation of military excellence and (...) the fun produced by drinking, music and dance. (shrink)

In [3] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of (...) jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to “second quantization.” As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a distributional semantic model, here exemplified by bidirectional encoder representations from transformers (BERT), represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping between CHICKEN (as an animal) and CHICKEN (as a meat) similar to that which maps between (...) LOBSTER (as an animal) to LOBSTER (as a meat)?” We did so using the LRcos model, which combines a logistic regression classifier of different categories (e.g., animal vs. meat) with a measure of cosine similarity. We found that (a) the model was sensitive to the shared structure within a given regular relationship; (b) the shared structure varies across different regular relationships (e.g., animal/meat vs. location/organization), potentially reflective of a “regularity continuum;” (c) some high-order latent structure is shared across different regular relationships, suggestive of a similar latent structure across different types of relationships; and (d) there is a lack of evidence for the aforementioned effects being explained by meaning overlap. Lastly, we found that both components of the LRcos model made important contributions to accurate responding and that a variation of this method could yield an accuracy boost of 10% in answering sense analogy questions. These findings enrich previous theoretical work on regular polysemy with a computationally explicit theory and methods, and provide evidence for an important organizational principle for the mental lexicon and the broader conceptual knowledge system. (shrink)

Debunking arguments are arguments that seek to undermine a belief or doctrine by exposing its causal origins. Two prominent proponents of such arguments are the utilitarians Joshua Greene and Peter Singer. They draw on evidence from moral psychology, neuroscience, and evolutionary theory in an effort to show that there is something wrong with how deontological judgments are typically formed and with where our deontological intuitions come from. They offer debunking explanations of our emotion-driven deontological intuitions and dismiss complex deontological theories (...) as products of confabulatory post hoc rationalization. Through my discussion of Greene and Singer’s empirically informed debunking of deontology, I introduce the distinction between two different types of debunking arguments. The first type of debunking argument operates through regular undercutting defeat, whereas the second type relies on higher-order evidence. I argue that the latter type of debunking argument, of which the argument from confabulation is an example, is objectionably sloppy and therefore inadmissible in academic discussion. (shrink)

It is a crucial issue for history to determine a cause or a causal relation between two events. The regularity theory of causation is one of the most popular approach to this problem. The paper analyzes mainly how this approach deals with the determination of a causal condition and with the choice of the main cause from the remaining causal conditions. It examines also Mackie’s conception of cause as an INUS condition, which is in fact only one version of the (...) regularity theory. The paper not only outlines and illustrates these approaches, using a concrete causal statments, but also presents the criticism of their shortcomings. It points to their difficulties springing from their inability to distinguish between the laws and accidental generalizations. This is important, because a genuine causal relation cannot be based on the second type of statments. (shrink)

There is a type of explanation frequently employed in the sciences, particularly the quantitative ones, that I intend to focus on. It seeks to understand some phenomenon or regularity that occurs in a type of system S by deriving an equation describing that phenomenon or regularity from a set of equations that govern S. I want to propose a way of understanding such explanations.

Traditionally, in the literature on robustness analysis objects are classified as genuine phenomena (natural objects, events, and processes) or artifacts (results produced in error). But much of biological measurement requires the manipulation of local experimental conditions in order to produce new effects. These types of intervention-based regularities are neither natural objects nor artifacts; characterizing them as either fails adequately to address key ontological properties as well as their role in scientific practice. It is argued that a new classification, based (...) on methodological considerations, can be useful in order to characterize experimental productions. Experimentally-useful context-sensitive objects are referred to as ‘artefacts’. To show how the new classification works and why it is instructive for scientific practice, two case studies are discussed. First, the puzzle of arsenic-consuming living organisms is analyzed, where under a set of specific experimental conditions a given organism was found to replace phosphorous with arsenic in its DNA. Second, ecological epigenetic measurement is discussed to show the complexity of variant effects in the context of lab, field, and computer measurements. It is argued that the line between artifacts and artefacts is fluid because theoretical, experimental, and practical considerations vary. (shrink)

This narrative review of the literature assessed whether regular physical exercise and sleep patterns, fasting and autophagy, altogether can be an adequate strategy for achieving healthy longevity and well-being within different stage of life. There are a large number of studies dealing with well-being and healthy longevity; however, few of them have given us a specific formula for how to live long and healthy. Despite all the advances that have been made to create adequate physical exercise programs, sleep patterns (...) or nutritional protocols, the relation between different types of fasting, nutritional supplementation as well as regular physical exercise and sleep patterns have not yet been satisfactorily resolved to cause the best effects of autophagy and, therefore, well-being and healthy longevity. In this way, future studies should clarify more efficiently the relationship between these variables to understand the association between regular physical exercise, sleep patterns, fasting and autophagy for healthy longevity and well-being. (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this article argues that the recent regularity-theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, it is shown that (...) a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world’s causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

This is an abstract of the paper to be submitted to Houston Journal of Mathematics. Our nomenclature and notation will be basically those of [3]. We shall consider algebras of type : T ! N, where T is a nonempty set, and N the set of all positive integers. By V we denote the set of all variables occurring in a polynomial symbol p. An identity p = q is called strongly non-regular if it is of the form p (...) = x for some binary polynomial symbol p, such that x; y 2 V and x =6 y. Let R denote the set of all regular identities of type . If K is a class of algebras of type , then E denotes the set of all identities satised by all algebras in K. We put R = E \ R. A variety K is called strongly non-regular if E contains some strongly non-regular identity. If is a set of identities of type , then K denotes the variety of algebras of type generated by ; E() will be the set of all identities which are consequences of . We put R() = E() \ R. We write ` e if there exists a nite proof of e starting from. (shrink)

Learning a mapping involves finding regularities in a training set and generalization to novel patterns. Clark & Thornton's type distinction has been discussed in terms of generalization, but has limited value in this respect. However, in terms of detection of regularities in the training set, the distinction is more valid, as it provides a measure of complexity and correlates with the size of search space.

We introduce notions of strong and eventual strong non-isolation for types in countable, stable theories. For T superstable or small stable we prove a dichotomy theorem: a regular type over a finite domain is either eventually strongly non-isolated or is non-orthogonal to a NENI type . As an application we obtain the upper bound for Lascar’s rank of a superstable theory which is one-based or trivial, and has fewer than 20 non-isomorphic countable models.

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this paper argues that the recent regularity theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, it is shown (...) that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world's causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

One of the chief difficulties we encounter as modern readers in perceiving the artistry of biblical narrative is precisely that we have lost most of the keys to the conventions out of which it was shaped. The professional Bible scholars have not offered much help in this regard, for their closest approximation to the study of convention is form criticism, which is set on finding recurrent regularities of pattern rather than the manifold variations upon a pattern that any system of (...) literary convention elicits; moreover, form criticism uses these patterns for excavative ends to support hypotheses about the social functions of the text, its historical evolution, and so forth. . . . The most crucial case in point is the perplexing fact that in biblical narrative more or less the same story often seems to be told two or three or more times about different characters, or sometimes even about the same character in different sets of circumstances. Three times a patriarch is driven by famine to a southern region where he pretends that his wife is his sister, narrowly avoids a violation of the conjugal bond by the local ruler, and is sent away with gifts. Twice Hagar flees into the wilderness from Sarah's hostility and discovers a miraculous well, and that story itself seems only a special variation of the recurrent story of bitter rivalry between a barren, favored wife and a fertile co-wife or concubine. That situation, in turn, suggests another oft-told tale in the Bible, of a woman long barren who is vouchsafed a divine promise of progeny, whether by God himself or through a divine messenger or oracle, and who then gives birth to a hero. Robert Alter, professor of Hebrew and comparative literature at the University of California at Berkeley, is the author of, among other works, Partial Magic: The Novel as a Self-Conscious Genre and Defenses of the Imagination. He has written a general literary study of biblical narrative, of which this essay forms a chapter. (shrink)

We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if is a regular ultrafilter on λ such that and M is a model whose theory is countable, then is λ+-saturated iff it realizes all φ-types of size λ.

A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and (...) kinematic geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge. Key Words: internalization of regularities; kinematic geometry; simplicity. (shrink)

König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a higher Souslin tree from the strong guessing principle.Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with a successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for the construction of a (...) higher Souslin tree.We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper. (shrink)

This paper examines whether adults can adapt to novel accents of their native language that contain unfamiliar context-dependent phonological alternations. In two experiments, French participants listen to short stories read in accented speech. Their knowledge of the accents is then tested in a forced-choice identification task. In Experiment 1, two groups of listeners are exposed to newly created French accents in which certain vowels harmonize or disharmonize, respectively, to the rounding of the preceding vowel. Despite the cross-linguistic predominance of vowel (...) harmony over disharmony, the two groups adapt equally well to both accents, suggesting that this typological difference is not reflected in perceptual learning. Experiment 2 further explores the mechanism underlying this type of phonological learning. Participants are exposed to an accent in which some vowels harmonize and others disharmonize, yielding an increased featural complexity. They adapt less well to this regularity, showing that adaptation to novel accents involves feature-based inferences. (shrink)

Historical narration is a system of mental operations defining the field of historical consciousness. It is poetic in that it is the performance of creative activity by the human mind in the process of historical thinking. The purpose of historical narration is to make sense of the experience of time in order to orient practical life in the course of time. Three elements distinguish an historical narration from other forms of narration: an historical narration is tied to the medium of (...) memory; it organizes the three dimensions of time in a concept of continuity; and it establishes the identity of its authors and listeners. In order to develop the concepts of continuity and the stability of identity, an historical narration must fulfill four functions: affirmation, regularity, negation, and transformation. Four types of historical narration correspond to these four functions: traditional, exemplary, critical, and genetical. There is a natural progression through these four types of narration, with critical narration serving as a catalyst. The four types are present in all historical texts, one dominating, the others secondary. Modern historical studies are unique in being informed by theoretically and methodologically organized empirical research. The articulation of theories in history means a progress in reasoning. This affects the role of the concept of continuity of time, which is no longer a given and has become a subject of discussion. (shrink)

Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asserting inhabitation of an indexed family. We give rules for bracket types in dependent type theory and provide complete (...) semantics using regular categories. We show that dependent type theory with the unit type, strong extensional equality types, strong dependent sums, and bracket types is the internal type theory of regular categories, in the same way that the usual dependent type theory with dependent sums and products is the internal type theory of locally Cartesian closed categories. We also show how to interpret first-order logic in type theory with brackets, and we make use of the translation to compare type theory with logic. Specifically, we show that the propositions-as-types interpretation is complete with respect to a certain fragment of intuitionistic first-order logic, in the sense that a formula from the fragment is derivable in intuitionistic first-order logic if, and only if, its interpretation in dependent type theory is inhabited. As a consequence, a modified double-negation translation into type theory (without bracket types) is complete, in the same sense, for all of classical first-order logic. (shrink)

For each regular cardinal κ, we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are $\Sigma _{}$, the global system $\text{g}\Sigma _{}$ and the τ-system $\tau \Sigma _{}$. A full cut elimination theorem is proved for the local systems, and about the τ-systems we prove that they admit cut-free proofs for sequents in the τ-free language common to the local and global systems. These (...) two results follow from semantic completeness proofs. Thus every sequent provable in a global system has a cut-free proof in the corresponding τ-systems. It is, however, an open question whether the global systems in themselves admit cut elimination. (shrink)

Most defenders of the new mechanistic approach accept ontic constraints for successful scientific explanation (Illari 2013; Craver 2014). The minimal claim is that scientific explanations have objective truthmakers, namely mechanisms that exist in the physical world independently of any observer and that cause or constitute the phenomena-to- be-explained. How can this idea be applied to type-level explanations? Many authors at least implicitly assume that in order for mechanisms to be the truthmakers of type-level explanation they need to be regular (...) (Andersen 2012; Sheredos 2015). One problem of this assumption is that most mechanisms are (highly) stochastic in the sense that they “fail more often than they succeed” (Bogen 2005; Andersen 2012). How can a mechanism type whose instances are more likely not to produce an instance of a particular phenomenon type be the truthmaker of the explanation of that particular phenomenon type? In this paper, I will give an answer to this question. I will analyze the notion of regularity and I will discuss Andersen's suggestion for how to cope with stochastic mechanisms. I will argue that her suggestion cannot account for all kinds of stochastic mechanisms and does not provide an answer as to why regularity grounds type-level explanation. According to my analysis, a mechanistic type- level explanation is true if and only if at least one of the following two conditions is satisfied: the mechanism brings about the phenomenon more often than any other phenomenon (comparative regularity) or the phenomenon is more often brought about by the mechanism than by any other mechanism/causal sequence (comparative reverse regularity). (shrink)

A method of iteration of Prikry type forcing notions as well as a forcing for adding clubs is presented. It is applied to construct a model with a measurable cardinal containing a club of former regulars, starting with o(κ) = κ + 1. On the other hand, it is shown that the strength of above is at least o(κ) = κ.