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The Disjunction and Related Properties for Constructive Zermelo-Fraenkel Set Theory

Michael Rathjen
The Journal of Symbolic Logic
Vol. 70, No. 4 (Dec., 2005), pp. 1233-1254
Stable URL: http://www.jstor.org/stable/27588423
Page Count: 22
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The Disjunction and Related Properties for Constructive Zermelo-Fraenkel Set Theory
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Abstract

This paper proves that the disjunction property, the numerical existence property. Church's rule, and several other metamathematical properties hold true for Constructive Zermelo-Fraenkel Set Theory. CZF. and also for the theory CZF augmented by the Regular Extension Axiom. As regards the proof technique, it features a self-validating semantics for CZF that combines realizability for extensional set theory and truth.

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