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The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability

Published online by Cambridge University Press:  12 March 2014

Eugenio Omodeo  and
Alberto Policriti
Eugenio Omodeo
Affiliation:
Dipartimento di Matematica e Informatica, Università di Trieste, 34127, Via Valerio 12/B, Italy. E-mail: eomodeo@units.it
Alberto Policriti
Affiliation:
Dipartimento di Matematica e Informatica, Università di Udine, 33100, Via Delle Scienze 206, Italy. E-mail: policriti@dimi.uniud.it
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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.

Keywords

Satisfiabilitydecision and semi-decision algorithmscomputable set theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 459 - 480
Copyright
Copyright © Association for Symbolic Logic 2010

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