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

Journal of Symbolic Logic 70 (4):1233 - 1254 (2005)
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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DOI 10.2178/jsl/1129642124
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References found in this work BETA
The Strength of Some Martin-Löf Type Theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Inaccessible Set Axioms May Have Little Consistency Strength.L. Crosilla & M. Rathjen - 2002 - Annals of Pure and Applied Logic 115 (1-3):33-70.
Realizability and Recursive Set Theory.Charles McCarty - 1986 - Annals of Pure and Applied Logic 32 (2):153-183.

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Citations of this work BETA
From the Weak to the Strong Existence Property.Michael Rathjen - 2012 - Annals of Pure and Applied Logic 163 (10):1400-1418.
CZF Does Not Have the Existence Property.Andrew W. Swan - 2014 - Annals of Pure and Applied Logic 165 (5):1115-1147.
Refinement is Equivalent to Fullness.Albert Ziegler - 2010 - Mathematical Logic Quarterly 56 (6):666-669.

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