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The disjunction and related properties for constructive Zermelo-Fraenkel set theory

Published online by Cambridge University Press:  12 March 2014

Michael Rathjen
Michael Rathjen*
Affiliation:
Department of Mathematics, Ohio State University, Columbus. OH 43210., USA, E-mail: rathjen@math.ohio-state.edu
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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.

Keywords

Constructive set theoryrealizabilitymetamathematical property

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1233 - 1254
Copyright
Copyright © Association for Symbolic Logic 2005

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