The Bernays—Schönfinkel—Ramsey class for set theory: decidability
Eugenio Omodeo and Alberto Policriti
Source: J. Symbolic Logic Volume 77, Issue 3
(2012), 896-918.
Abstract
As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays—Shönfinkel—Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1344862166
Digital Object Identifier: doi:10.2178/jsl/1344862166
Mathematical Reviews number (MathSciNet): MR2987142
References
Egon Börger, Erich Grädel, and Yuri Gurevich The classical decision problem, Perspectives in Mathematical Logic, Springer,1997.
Mathematical Reviews (MathSciNet): MR1482227
D. Cantone, E. G. Omodeo, and A. Policriti Set theory for computing. From decision procedures to declarative programming with sets, Monographs in Computer Science, Springer-Verlag,2001.
Mathematical Reviews (MathSciNet): MR1892431
Zentralblatt MATH: 0981.03056
A. Dovier, E. G. Omodeo, E. Pontelli, and G.-F. Rossi A language for programming in logic with finite sets, Journal of Logic Programming, vol. 28(1996), no. 1, pp. 1–44.
K. Kunen Set theory: an introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, Elsevier,1983.
Mathematical Reviews (MathSciNet): MR756630
E. G. Omodeo and A. Policriti The Bernays–Schönfinkel–Ramsey class for set theory: Semidecidability, Journal of Symbolic Logic, vol. 75(2010), no. 2, pp. 459–480.
Mathematical Reviews (MathSciNet): MR2648151
Digital Object Identifier: doi:10.2178/jsl/1268917490
Project Euclid: euclid.jsl/1268917490
E. G. Omodeo, A. Policriti, and A. I. Tomescu Infinity, in short, Journal of Logic and Computation, in press, DOI: 10.1093/logcom/exr020.
F. Parlamento and A. Policriti The logically simplest form of the infinity axiom, Proceedings of the American Mathematical Society, vol. 103(1988), no. 1, pp. 274–276.
Mathematical Reviews (MathSciNet): MR938682
Digital Object Identifier: doi:10.1090/S0002-9939-1988-0938682-2
F. P. Ramsey On a problem of formal logic, Proceedings of the London Mathematical Society, vol. 30(1930), pp. 264–286, read on December 13, 1928.
Mathematical Reviews (MathSciNet): MR1576401
Digital Object Identifier: doi:10.1112/plms/s2-30.1.264