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June 2013 Satisfaction relations for proper classes: applications in logic and set theory
Robert A. Van Wesep
J. Symbolic Logic 78(2): 345-368 (June 2013). DOI: 10.2178/jsl.7802010

Abstract

We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate ($\models^*$) appropriate to such structures. We indicate the utility of this theory as a framework for the development of the metatheory of first-order predicate logic and set theory, and we use it to prove that for any recursively enumerable extension $\Theta$ of ZF there is a finitely axiomatizable extension $\Theta'$ of GB that is a conservative extension of $\Theta$. We also prove a conservative extension result that justifies the use of $\models^*$ to characterize ground models for forcing constructions.

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Robert A. Van Wesep. "Satisfaction relations for proper classes: applications in logic and set theory." J. Symbolic Logic 78 (2) 345 - 368, June 2013. https://doi.org/10.2178/jsl.7802010

Information

Published: June 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1278.03077
MathSciNet: MR3145185
Digital Object Identifier: 10.2178/jsl.7802010

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 2 • June 2013
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