Annals of Pure and Applied Logic, ISSN 0168-0072, 04/2013, Volume 164, Issue 4, pp. 396 - 415

The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory (CST). Arithmetical CST is just...

Constructive set theory | Rudimentary functions | Arithmetic | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Constructive set theory | Rudimentary functions | Arithmetic | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Outstanding Contributions to Logic, ISSN 2211-2758, 2017, Volume 13, pp. 491 - 523

Journal Article

2011, ISBN 1420093649, xxv, 893

Book

Theoretical Computer Science, ISSN 0304-3975, 04/2011, Volume 412, Issue 20, pp. 1916 - 1940

One of the main goals of this paper is to give a construction of realizability models for predicative constructive set theories in a predicative metatheory. We...

Categorical logic | Constructive set theory | Realizability | EFFECTIVE TOPOS | COMPUTER SCIENCE, THEORY & METHODS | Construction | Algebra | Maps | Axioms | Categories | Set theory | Mathematical models | Assemblies

Categorical logic | Constructive set theory | Realizability | EFFECTIVE TOPOS | COMPUTER SCIENCE, THEORY & METHODS | Construction | Algebra | Maps | Axioms | Categories | Set theory | Mathematical models | Assemblies

Journal Article

2016, Lecture notes in logic, ISBN 131671831X, Volume 3

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original...

Constructive mathematics | Set theory

Constructive mathematics | Set theory

Web Resource

2016, Lecture Notes in Logic, ISBN 9781316768174, Volume 3

Web Resource

Annals of Pure and Applied Logic, ISSN 0168-0072, 10/2012, Volume 163, Issue 10, pp. 1367 - 1383

We show how one may establish proof-theoretic results for constructive Zermelo–Fraenkel set theory, such as the compactness rule for Cantor space and the Bar...

Derived rules | Sheaves | Baire space | Constructive set theory | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | EXACT COMPLETION | LOGIC

Derived rules | Sheaves | Baire space | Constructive set theory | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | EXACT COMPLETION | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 02/2014, Volume 165, Issue 2, pp. 563 - 572

In recent years the question of whether adding the limited principle of omniscience, , to constructive Zermelo–Fraenkel set theory, , increases its strength...

Constructive set theory | Proof-theoretic strength | Limited principle of omniscience | Bar induction | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Constructive set theory | Proof-theoretic strength | Limited principle of omniscience | Bar induction | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2012, Volume 163, Issue 2, pp. 175 - 184

This article presents a common generalization of the two main methods for obtaining class models of constructive set theory. Heyting models are a...

Formal topology | Pca’s | Constructive set theory | Heyting models | CZF | Realizability | Pca's | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Formal topology | Pca’s | Constructive set theory | Heyting models | CZF | Realizability | Pca's | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 12/2013, Volume 164, Issue 12, pp. 1274 - 1292

The paper aims to provide precise proof theoretic characterizations of Myhill–Friedman-style “weak” constructive extensional set theories and Aczel–Rathjen...

Set theory | Proof theory | Constructive mathematics | Classical and intuitionistic mathematical logic | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Set theory | Proof theory | Constructive mathematics | Classical and intuitionistic mathematical logic | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 12/2007, Volume 150, Issue 1-3, pp. 19 - 39

We study OST and some of its most important extensions primarily from a proof-theoretic perspective, determine their consistency strengths by exhibiting...

Operational set theory | Proof theory | Classical and constructive set theories | Explicit mathematics | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | operational set theory | explicit mathematics | classical and constructive set theories | proof theory

Operational set theory | Proof theory | Classical and constructive set theories | Explicit mathematics | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | operational set theory | explicit mathematics | classical and constructive set theories | proof theory

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2006, Volume 137, Issue 1, pp. 3 - 29

Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general...

Formal topology | Locale | Constructive set theory | Constructive mathematics | General topology | MATHEMATICS | general topology | MATHEMATICS, APPLIED | constructive mathematics | constructive set theory | locale | POINTS | LOGIC | formal topology

Formal topology | Locale | Constructive set theory | Constructive mathematics | General topology | MATHEMATICS | general topology | MATHEMATICS, APPLIED | constructive mathematics | constructive set theory | locale | POINTS | LOGIC | formal topology

Journal Article

Journal of Mathematical Logic, ISSN 0219-0613, 2014, Volume 14, Issue 1, pp. 1450005 - 1-1450005-28

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the...

sheaves | Constructive set theory | algebraic set theory | realizability | MATHEMATICS | LOGIC | Construction standards | Construction | Theorems | Algebra | Axioms | Mathematical logic | Set theory | Mathematical models

sheaves | Constructive set theory | algebraic set theory | realizability | MATHEMATICS | LOGIC | Construction standards | Construction | Theorems | Algebra | Axioms | Mathematical logic | Set theory | Mathematical models

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 10/2012, Volume 163, Issue 10, pp. 1419 - 1436

We define a to be a locally cartesian closed pretopos. The terminology is supported by the fact that constructive toposes enjoy a relationship with...

Categorical logic | Sheaves | Constructive set theory | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Categorical logic | Sheaves | Constructive set theory | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2006, Volume 137, Issue 1, pp. 164 - 188

We define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory (CZF). These interpretations provide models for CZF that...

Formal topology | Heyting algebra | Frame | Constructive set theory | Heyting-valued models | Pointfree topology | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | pointfree topology | constructive set theory | LOGIC | formal topology | frame

Formal topology | Heyting algebra | Frame | Constructive set theory | Heyting-valued models | Pointfree topology | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | pointfree topology | constructive set theory | LOGIC | formal topology | frame

Journal Article

Journal of Symbolic Logic, ISSN 0022-4812, 09/2018, Volume 83, Issue 3, pp. 1132 - 1146

We give a model of set theory based on multisets in homotopy type theory. The equality of the model is the identity type. The underlying type of iterative sets...

W-types | phrasesconstructive set theory | type theory | homotopy type theory | higher inductive types | multisets | MATHEMATICS | constructive set theory | LOGIC

W-types | phrasesconstructive set theory | type theory | homotopy type theory | higher inductive types | multisets | MATHEMATICS | constructive set theory | LOGIC

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2008, Volume 156, Issue 1, pp. 123 - 159

This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on...

Categorical logic | Constructive set theory | Exact completion | MATHEMATICS | TOPOSES | CHOICE | MATHEMATICS, APPLIED | MODELS | CATEGORIES | AXIOM | LOGIC

Categorical logic | Constructive set theory | Exact completion | MATHEMATICS | TOPOSES | CHOICE | MATHEMATICS, APPLIED | MODELS | CATEGORIES | AXIOM | LOGIC

Journal Article

Mathematical Logic Quarterly, ISSN 0942-5616, 02/2008, Volume 54, Issue 1, pp. 83 - 97

Constructive set theory started with Myhill's seminal 1975 article [8]. This paper will be concerned with axiomatizations of the natural numbers in...

functional interpretation | Constructive set theory | proof‐theoretic strength | recursively saturated models | natural number object | Proof-theoretic strength | Recursively saturated models | Natural number object | Functional interpretation | MATHEMATICS | constructive set theory | proof-theoretic strength

functional interpretation | Constructive set theory | proof‐theoretic strength | recursively saturated models | natural number object | Proof-theoretic strength | Recursively saturated models | Natural number object | Functional interpretation | MATHEMATICS | constructive set theory | proof-theoretic strength

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2006, Volume 141, Issue 1, pp. 257 - 265

The standard construction of quotient spaces in topology uses full separation and power sets. We show how to make this construction using only the...

Constructive topology | Constructive set theory | Martin-Löf type theory | Quotient spaces | MATHEMATICS | MATHEMATICS, APPLIED | constructive set theory | STRENGTH | quotient spaces | constructive topology | Martin-Lof type theory

Constructive topology | Constructive set theory | Martin-Löf type theory | Quotient spaces | MATHEMATICS | MATHEMATICS, APPLIED | constructive set theory | STRENGTH | quotient spaces | constructive topology | Martin-Lof type theory

Journal Article

JOURNAL OF UNIVERSAL COMPUTER SCIENCE, ISSN 0948-695X, 2005, Volume 11, Issue 12, pp. 2008 - 2033

The paper furnishes realizability models of constructive Zermelo-Fraenkel set theory, CZF, which also validate Brouwerian principles such as the axiom of...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | Brouwerian principles | constructive set theory | COMPUTER SCIENCE, THEORY & METHODS | partial combinatory algebra | realizability

COMPUTER SCIENCE, SOFTWARE ENGINEERING | Brouwerian principles | constructive set theory | COMPUTER SCIENCE, THEORY & METHODS | partial combinatory algebra | realizability

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.