Journal of Symbolic Logic

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

Michael Rathjen

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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.

Article information

J. Symbolic Logic Volume 70, Issue 4 (2005), 1233-1254.

First available in Project Euclid: 18 October 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F50: Metamathematics of constructive systems 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]

Constructive set theory realizability metamathematical property


Rathjen, Michael. The disjunction and related properties for constructive Zermelo-Fraenkel set theory. J. Symbolic Logic 70 (2005), no. 4, 1233--1254. doi:10.2178/jsl/1129642124.

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