Switch to: References

Citations of:

The natural numbers in constructive set theory

Michael Rathjen

Mathematical Logic Quarterly 54 (1):83-97 (2008)

Add citations

You must login to add citations.

Fragments of Kripke–Platek set theory and the metamathematics of $$\alpha $$ α -recursion theory.Sy-David Friedman, Wei Li & Tin Lok Wong - 2016 - Archive for Mathematical Logic 55 (7-8):899-924.details The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in $$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} (...) Download Export citation Bookmark 3 citations
Constructive Ackermann's interpretation.Hanul Jeon - 2022 - Annals of Pure and Applied Logic 173 (5):103086.details Download Export citation Bookmark
Extending constructive operational set theory by impredicative principles.Andrea Cantini - 2011 - Mathematical Logic Quarterly 57 (3):299-322.details We study constructive set theories, which deal with operations applying both to sets and operations themselves. Our starting point is a fully explicit, finitely axiomatized system ESTE of constructive sets and operations, which was shown in 10 to be as strong as PA. In this paper we consider extensions with operations, which internally represent description operators, unbounded set quantifiers and local fixed point operators. We investigate the proof theoretic strength of the resulting systems, which turn out to be impredicative . (...) Download Export citation Bookmark 3 citations
Rudimentary and arithmetical constructive set theory.Peter Aczel - 2013 - Annals of Pure and Applied Logic 164 (4):396-415.details The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory . Arithmetical CST is just strong enough to represent the class of von Neumann natural numbers and its arithmetic so as to interpret Heyting Arithmetic. Rudimentary CST is a very weak subsystem that is just strong enough to represent a constructive version of Jensenʼs rudimentary set theoretic functions and their theory. The paper is a contribution to the study (...) Download Export citation Bookmark 2 citations
Set theory: Constructive and intuitionistic ZF.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.details Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic logic. They were introduced in the 1970's and they represent a formal context within which to codify mathematics based on intuitionistic logic. They are formulated on the basis of the standard first order language of Zermelo-Fraenkel set theory and make no direct use of inherently constructive ideas. In working in constructive and intuitionistic ZF we can thus (...) Download Export citation Bookmark 4 citations

1