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June 2010 The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability
Eugenio Omodeo, Alberto Policriti
J. Symbolic Logic 75(2): 459-480 (June 2010). DOI: 10.2178/jsl/1268917490

Abstract

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃**-sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper.

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Eugenio Omodeo. Alberto Policriti. "The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability." J. Symbolic Logic 75 (2) 459 - 480, June 2010. https://doi.org/10.2178/jsl/1268917490

Information

Published: June 2010
First available in Project Euclid: 18 March 2010

zbMATH: 1201.03007
MathSciNet: MR2648151
Digital Object Identifier: 10.2178/jsl/1268917490

Keywords: computable set theory , decision and semi-decision algorithms , satisfiability

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 2 • June 2010
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