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Spring 1995 Decidability and Completeness for Open Formulas of Membership Theories
Dorella Bellè, Franco Parlamento
Notre Dame J. Formal Logic 36(2): 304-318 (Spring 1995). DOI: 10.1305/ndjfl/1040248461


We establish the decidability, with respect to open formulas in the first order language with equality =, the membership relation $\in$, the constant $\emptyset$ for the empty set, and a binary operation w which, applied to any two sets x and y, yields the results of adding y as an element to x, of the theory NW having the obvious axioms for $\emptyset$ and w. Furthermore we establish the completeness with respect to purely universal sentences of the theory $\mbox{NW}+\mbox{E}+\mbox{R}$, obtained from NW by adding the Extensionality Axiom E and the Regularity Axiom R, and of the theory $\mbox{NW}+\mbox{AFA}'$ obtained by adding to NW (a slight variant of) the Antifoundation Axiom AFA.


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Dorella Bellè. Franco Parlamento. "Decidability and Completeness for Open Formulas of Membership Theories." Notre Dame J. Formal Logic 36 (2) 304 - 318, Spring 1995.


Published: Spring 1995
First available in Project Euclid: 18 December 2002

zbMATH: 0837.03007
MathSciNet: MR1345751
Digital Object Identifier: 10.1305/ndjfl/1040248461

Primary: 03E30
Secondary: 03B25, 03C62

Rights: Copyright © 1995 University of Notre Dame


Vol.36 • No. 2 • Spring 1995
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