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

Journal of Symbolic Logic 70 (4):1233 - 1254 (2005)
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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DOI 10.2307/27588423
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Michael Rathjen (2012). From the Weak to the Strong Existence Property. Annals of Pure and Applied Logic 163 (10):1400-1418.
Albert Ziegler (2010). Refinement is Equivalent to Fullness. Mathematical Logic Quarterly 56 (6):666-669.
Andrew W. Swan (2014). CZF Does Not Have the Existence Property. Annals of Pure and Applied Logic 165 (5):1115-1147.

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