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Heyting-valued interpretations for constructive set theory
Annals of Pure and Applied Logic 137 (1-3):164-188 (2006)
Abstract
We define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory . These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proofLinks
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Citations of this work
Aspects of predicative algebraic set theory I: Exact Completion.Benno van den Berg & Ieke Moerdijk - 2008 - Annals of Pure and Applied Logic 156 (1):123-159.
The Generalised Type-Theoretic Interpretation of Constructive Set Theory.Nicola Gambino & Peter Aczel - 2006 - Journal of Symbolic Logic 71 (1):67 - 103.
Derived rules for predicative set theory: an application of sheaves.Benno van den Berg & Ieke Moerdijk - 2012 - Annals of Pure and Applied Logic 163 (10):1367-1383.
Set theory: Constructive and intuitionistic ZF.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.
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Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1981 - Journal of Symbolic Logic 46 (1):165-165.
Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
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