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2001 The Decidability of the $ \forall^*\exists$ Class and the Axiom of Foundation
Dorella Bellè, Franco Parlamento
Notre Dame J. Formal Logic 42(1): 41-53 (2001). DOI: 10.1305/ndjfl/1054301354

Abstract

We show that the Axiom of Foundation, as well as the Antifoundation Axiom AFA, plays a crucial role in determining the decidability of the following problem. Given a first-order theory T over the language $ =,\in$, and a sentence F of the form $ \forall x_1, \ldots, x_n \exists y F^M$ with $ F^M$ quantifier-free in the same language, are there models of T in which F is true? Furthermore we show that the Extensionality Axiom is quite irrelevant in that respect.

Citation

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Dorella Bellè. Franco Parlamento. "The Decidability of the $ \forall^*\exists$ Class and the Axiom of Foundation." Notre Dame J. Formal Logic 42 (1) 41 - 53, 2001. https://doi.org/10.1305/ndjfl/1054301354

Information

Published: 2001
First available in Project Euclid: 30 May 2003

zbMATH: 1023.03007
MathSciNet: MR1993389
Digital Object Identifier: 10.1305/ndjfl/1054301354

Subjects:
Primary: 03B25, 03C62
Secondary: 03E50

Rights: Copyright © 2001 University of Notre Dame

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