Can You Add Power‐Sets to Martin‐Lof's Intuitionistic Set Theory?

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Mathematical Logic Quarterly 45 (4):521-532 (1999)
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Abstract

In this paper we analyze an extension of Martin-Löf s intensional set theory by means of a set contructor P such that the elements of P are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this extension is classic, that is “ true holds for any proposition A

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10.1002/malq.19990450410

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Citations of this work

A minimalist two-level foundation for constructive mathematics.Maria Emilia Maietti - 2009 - Annals of Pure and Applied Logic 160 (3):319-354.
Formal Zariski topology: positivity and points.Peter Schuster - 2006 - Annals of Pure and Applied Logic 137 (1-3):317-359.

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References found in this work

Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Toposes and Local Set Theories. An Introduction.J. L. Bell - 1990 - Journal of Symbolic Logic 55 (2):886-887.
The inconsistency of higher order extensions of Martin-löf's type theory.Bart Jacobs - 1989 - Journal of Philosophical Logic 18 (4):399 - 422.
Axiom of Choice and Complementation.Radu Diaconescu - 1975 - Proceedings of the American Mathematical Society 51 (1):176-178.

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