Results 261 to 270 of about 37,312 (297)

The natural numbers in constructive set theory

Mathematical Logic Quarterly, 2008
AbstractConstructive set theory started with Myhill's seminal 1975 article [8]. This paper will be concerned with axiomatizations of the natural numbers in constructive set theory discerned in [3], clarifying the deductive relationships between these axiomatizations and the strength of various weak constructive set theories.
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A Constructive Morse Theory of Sets

1987
In this paper I shall outline a foundational system for constructive mathematics analogous to that given in [11] for classical mathematics. By ‘constructive mathematics’ I shall mean mathematics as understood by Errett Bishop and his followers [2, 3], the mathematics of which the primary concern … is number, and this means the positive integers ...
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Hereditarily Finite Sets in Constructive Type Theory

2016
We axiomatize hereditarily finite sets in constructive type theory and show that all models of the axiomatization are isomorphic. The axiomatization takes the empty set and adjunction as primitives and comes with a strong induction principle. Based on the axiomatization, we construct the set operations of ZF and develop the basic theory of finite ...
Gert Smolka, Kathrin Stark
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Set theory with free construction principles

1983
In set theory with the axiom of foundation, the \(\in\)-relations on transitive classes are up to isomorphism just the extensional well-founded relations. In the absence of the axiom of foundation one may require various axioms of universality (e.g. that every binary relation (which is extensional) has an homomorphism (an isomorphism, resp.) onto the \(
FORTI, MARCO, HONSELL F.
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A constructive set theory for program development

1988
We present a constructive theory of types and kinds (called TK5) designed with program development as the major desideratum. We motivate its definition with respect to existing research in the area of program logics (in particular Martin-Lof's theory of types) and establish suitable infrastructure for program extraction from proofs of specifications.
Martin C. Henson, Raymond Turner
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Set Theory: Constructive and Intuitionistic ZF

2009
Introduzione alla teoria costruttiva degli ...
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Constructive Hovels for Set Theory with Extensionalitv

1982
Publisher Summary This chapter discusses various constructive models for set theory with extensionality. There are two well-known methods that can be used to interpret J.Myhill-style extensional constructive set theories within subsystems of analysis and S.Feferman-style constructive systems of functions and classes.
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The Existence Property in Constructive Set Theory

1985
This chapter is primarily of technical interest, in the sense that nothing in the rest of the book depends upon it, and in the sense that the proofs are rather complicated. Nevertheless, the existence property has attracted considerable attention, since many people feel a constructive theory “ought to” have the existence property.
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Poly(ADP-Ribose) polymerase (PARP) inhibitors: Exploiting a synthetic lethal strategy in the clinic

Ca-A Cancer Journal for Clinicians, 2011
Timothy A Yap, Johann Sebastian de Bono
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Computational predictions of energy materials using density functional theory

Nature Reviews Materials, 2016
Anubhav Jain, Yongwoo Shin, Kristin A Persson   +2 more
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