Kripke models for subtheories of CZF

Archive for Mathematical Logic 49 (2):147-167 (2010)
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Abstract

In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold in the constructed Kripke model. It is shown that by carefully choosing the classical models various instances of the collection axioms, such as exponentiation, can be forced to hold as well. The paper does not contain any deep results. It consists of first observations on the subject, and is meant to introduce some notions that could serve as a foundation for further research

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Rosalie Iemhoff
Utrecht University

Citations of this work

Logics of intuitionistic Kripke-Platek set theory.Rosalie Iemhoff & Robert Passmann - 2021 - Annals of Pure and Applied Logic 172 (10):103014.
A Semantic Approach to Conservativity.Tomasz Połacik - 2016 - Studia Logica 104 (2):235-248.

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References found in this work

Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Independence results around constructive ZF.Robert S. Lubarsky - 2005 - Annals of Pure and Applied Logic 132 (2-3):209-225.
Heyting-valued interpretations for constructive set theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
CZF and second order arithmetic.Robert S. Lubarsky - 2006 - Annals of Pure and Applied Logic 141 (1):29-34.

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