The paper by Dupras and Bunnik is a useful addition to the literature on privacy in regards to datasets of human tissue/materials. In particular, the paper addresses import...

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...) λ = {α ∣Φ(λ, a)}. (shrink)

In addition to facing the known competitors in the formal economy, entrepreneurs must also be concerned with rivalry emanating from the informal economy. The informal economy is characterized by actions outside the normal scope of commerce, such as unsanctioned payments and gift-giving, as means of influencing competition. Scholars and policy makers alike have an interest in mitigating the impacts of such informal activity in that it might present an obstacle for legitimate commerce. Received theory suggests that country institutions can enable (...) and constrain productive activity, and, in doing so, influence competitive obstacles in a country. Leveraging 13,670 responses from entrepreneurs distributed across 59 countries, we provide evidence that two particular types of enabling institutions, countries’ property rights regulations and cooperative actions, are useful for lowering the obstacles presented by informal activity. We also find evidence that two constraining institutions, economic and financial regulations lead to more obstacles presented by informal activity. We describe implications for entrepreneurs, policy makers, and future researchers stemming from these findings. (shrink)

This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], as improved and extended by work of the second. We use the rudimentarily recursive functions and the slightly larger collection of gentle functions to initiate the study of provident sets, which are transitive models of $\mathsf{PROVI}$, a subsystem of $\mathsf{KP}$ whose minimal model is Jensen’s $J_{\omega}$. $\mathsf{PROVI}$ supports familiar definitions, such as rank, transitive closure and ordinal addition—though not ordinal multiplication—and Shoenfield’s unramified (...) forcing. Providence is preserved under directed unions. An arbitrary set has a provident closure, and the extension of a provident $M$ by a set-generic $\mathcal{G}$ is the provident closure of $M\cup\{\mathcal{G}\}$. The improvidence of many models of $\mathsf{Z}$ is shown. The final section uses similar but simpler recursions to show, in the weak system $\mathsf{MW}$, that the truth predicate for $\dot{\varDelta}_{0}$ formulæ is $\Delta_{1}$. (shrink)

Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.

Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha (...) \mid\Phi\}$. (shrink)

Dogmatic Metaphysics and Tschirnhaus's M ethodology MARTIN SCHONFELD ACCORDING TO STANDARD COMMENTARIES, Tschirnhaus's main work, Medicina mentis, ~ supposedly furnished the methodological basis for the Leibnizian-Wolffian metaphysics. ~ Christian Wolff and his disciples, at any rate, preferred to think so. Wolff taught classes on Tschirnhaus and claimed that he had developed his own tenets on the basis of Tschirnhaus's ideas; Johann Christoph Gottsched praised the Medicina mentis as the basic methodology of the Wolffian enlightenment.3 Mirroring these views, W. Wundt and (...) H. J. de Vleeschauwer saw in Tschirnhaus the inventor of the "geometric method" adopted by the School Philosophers.4 According to M. ' Medicina Mentis, sive Tentamen genuinae Logicae, in qua disseritur de Methodo detegendi incoKaitas veritates, Amsterdam, 1687. Second and revised edition, Medicina Mentis, sive Artis inveniendi Praecepta generalia, Leipzig, 1695. ~For example, cf. Wilhelm Windelband, Geschichte der Philosophie, 3~o-33 and 356; Friedrich Ueberweg, Grundriss der Geschichte der Philosophie, III: ~95-97, 3 x~ 34o-43; A. Robert Caponigri, A History of Western Philosophy (Notre Dame/London: University of Notre Dame.. (shrink)

We derive the schemes of from certain weak forms of the same.

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)

Rationale, aims and objectives This randomized controlled trial was designed to evaluate the 2-year costs and effects of a proactive, public health nursing case management approach compared with a self-directed approach for 129 single parents (98% were mothers) on social assistance in a Canadian setting. A total of 43% of these parents had a major depressive disorder and 38% had two or three other health conditions at baseline. Methods Study participants were recruited over a 12 month period and randomized into (...) two groups: one receiving proactive public health nursing and one which did not. Results At 2 years, 69 single parents with 123 children receiving proactive public health nursing (compared with 60 parents with 91 children who did not receive public health nursing services) showed a slightly greater reduction in dysthymia and slightly higher social adjustment. There was no difference between the public health and control groups in total per parent annual cost of health and support services. However, costs were averted due to a 12% difference in non-use of social assistance in the previous 12 months for parents in the public health nursing group. This translates into an annual cost saving of $240 000 (Canadian) of costs averted within 1 year for every 100 parents. Conclusions In the context of a system of national health and social insurance, this study supports the fact that it is no more costly to proactively service this population of parents on social assistance. (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)

We prove the existence of p-ideals that are nonmeagre subsets of P(ω) under various set-theoretic assumptions.

This is an encyclopedia entry (for the IVR Encyclopedia of legal and political philosophy) covering John Rawls. It aims to provide a general but not superficial introduction to Rawls's theory of justice, justice as fairness.

This is the introduction to the Ashgate volume on Rawls in their history of political thought series. It puts Rawls's life and work in context and then discusses the essays included in the volume, essays of high quality likely to shape scholarship on Rawls for the coming decades.

Dans ce volume considérable, on été réunies les contributions d'un Congrès international tenu à Louvain en 1998 pour marquer l'achèvement de la première édition de la Théologie Platonicienne de Proclus. Ces contributions, toutes rigoureusement centrées sur la Théol. Plat. concernent (1) les principes et les sources de la Théol. plat. (2) Les méthodes théologiques de Proclus (3) La postérité de la Théol. plat. dans le monde grec, païen comme chrétien, et dans le monde islamique. Des indices très détaillés permettent de (...) retrouver tous les passages cités et commentés dans ce volume. (shrink)