Large sets in intuitionistic set theory
Annals of Pure and Applied Logic 27 (1):1-24 (1984)
Abstract
We consider properties of sets in an intuitionistic setting corresponding to large cardinals in classical set theory. Adding such ‘large set axioms’ to intuitionistic ZF set theory does not violate well-know metamathematical properties of intuitionistic systems. Moreover, we consider statements in constructive analysis equivalent to the consistency of such ‘large set axioms’DOI
10.1016/0168-0072(84)90033-2
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Citations of this work
Non-classical foundations of set theory.Sourav Tarafder - 2022 - Journal of Symbolic Logic 87 (1):347-376.
Set theory: Constructive and intuitionistic zf.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.
Extensional Realizability and Choice for Dependent Types in Intuitionistic Set Theory.Emanuele Frittaion - forthcoming - Journal of Symbolic Logic:1-32.
References found in this work
The consistency of classical set theory relative to a set theory with intuitionistic logic.Harvey Friedman - 1973 - Journal of Symbolic Logic 38 (2):315-319.
Some applications of Kleene's methods for intuitionistic systems.Harvey Friedman - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 113--170.
Church's thesis, continuity, and set theory.M. Beeson & A. Ščedrov - 1984 - Journal of Symbolic Logic 49 (2):630-643.
