Large sets in intuitionistic set theory

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Annals of Pure and Applied Logic 27 (1):1-24 (1984)
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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’

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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.

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References found in this work

Some applications of Kleene's methods for intuitionistic systems.Harvey Friedman - 1973 - In A. R. D. Mathias & Hartley 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.

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