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)

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.

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

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)

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)

XLRI, in association with a few Tata Group companies, established the XLRI-JRD Tata Foundation in Business Ethics in 1991 to mark their long-standing commitment and contribution to business ethics in India. The foundation seeks to address this by publicly affirming the urgent need for ethics in business and the need to bring about a conducive culture in which it can thrive.

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

B. R. Frieden uses a single procedure, called extreme physical information, with the aim of deriving 'most known physics, from statistical mechanics and thermodynamics to quantum mechanics, the Einstein field equations and quantum gravity'. His method, which is based on Fisher information, is given a detailed exposition in this book, and we attempt to assess the extent to which he succeeds in his task.

Artificial intelligence plays an important role and has been used by several countries as a health strategy in an attempt to understand, control and find a cure for the disease caused by Coronavirus. These intelligent systems can assist in accelerating the process of developing antivirals for Coronavirus and in predicting new variants of this virus. For this reason, much research on COVID-19 has been developed with the aim of contributing to new discoveries about the Coronavirus. However, there are some epistemological (...) aspects about the use of AI in this pandemic period of Covid-19 that deserve to be discussed and need reflections. In this scenario, this article presents a reflection on the two epistemological aspects faced by the COVID-19 pandemic: The epistemological aspect resulting from the use of patient data to fill the knowledge base of intelligent systems; the epistemological problem arising from the dependence of health professionals on the results/diagnoses issued by intelligent systems. In addition, we present some epistemological challenges to be implemented in a pandemic period. (shrink)

A laboratory-testable, solid-state Maxwell demon is proposed that utilizes the electric field energy of an open-gap p-n junction. Numerical results from a commercial semiconductor device simulator (Silvaco International–Atlas) verify primary results from a 1-D analytic model. Present day fabrication techniques appear adequate for laboratory tests of principle.

Initial responses to questionnaires used to assess participants' understanding of informed consent for malaria vaccine trials conducted in the United States and Mali were tallied. Total scores were analyzed by age, sex, literacy (if known), and location. Ninety-two percent (92%) of answers by United States participants and 85% of answers by Malian participants were correct. Questions more likely to be answered incorrectly in Mali related to risk, and to the type of vaccine. For adult participants, independent predictors of higher scores (...) were younger age and female sex in the United States, and male sex in Mali. Scores in the United States were higher than in Mali (P = 0.005). Despite this difference participants at both sites were well informed overall. Although interpretation must be qualified because questionnaires were not intended as research tools and were not standardized among sites, these results do not support concerns about systematic low understanding among research participants in developing versus developed countries. (shrink)

Late in 1990, the Center for the Study of Ethics in the Professions at Illinois Institute of Technology (lIT) received a grant of more than $200,000 from the National Science Foundation to try a campus-wide approach to integrating professional ethics into its technical curriculum.! Enough has now been accomplished to draw some tentative conclusions. I am the grant's principal investigator. In this paper, I shall describe what we at lIT did, what we learned, and what others, especially philosophers, can learn (...) from us. We set out to develop an approach that others could profitably adopt. I believe that we succeeded. (shrink)

The US neutrino community gathered at the Workshop on the Intermediate Neutrino Program at Brookhaven National Laboratory February 4-6, 2015 to explore opportunities in neutrino physics over the next five to ten years. Scientists from particle, astroparticle and nuclear physics participated in the workshop. The workshop examined promising opportunities for neutrino physics in the intermediate term, including possible new small to mid-scale experiments, US contributions to large experiments, upgrades to existing experiments, R&D plans and theory. The workshop was organized into (...) two sets of parallel working group sessions, divided by physics topics and technology. Physics working groups covered topics on Sterile Neutrinos, Neutrino Mixing, Neutrino Interactions, Neutrino Properties and Astrophysical Neutrinos. Technology sessions were organized into Theory, Short-Baseline Accelerator Neutrinos, Reactor Neutrinos, Detector R&D and Source, Cyclotron and Meson Decay at Rest sessions.This report summarizes discussion and conclusions from the workshop. (shrink)

We discuss potential biorisks from large language models (LLMs). AI assistants based on LLMs such as ChatGPT have been shown to significantly reduce barriers to entry for actors wishing to synthesize dangerous, potentially novel pathogens and chemical weapons. The harms from deploying such bioagents could be further magnified by AI-assisted misinformation. We endorse several policy responses to these dangers, including prerelease evaluations of biomedical AIs by subject-matter experts, enhanced surveillance and lab screening procedures, restrictions on AI training data, and access (...) controls on biomedical AI. We conclude with a suggestion about future research directions in bioethics. (shrink)