### The Decidability of the Class and the Axiom of Foundation

Dorella Bellè and Franco Parlamento
Source: Notre Dame J. Formal Logic Volume 42, Number 1 (2001), 41-53.

#### 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 , and a sentence F of the form with 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.

First Page:
Primary Subjects: 03B25, 03C62
Secondary Subjects: 03E50
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1054301354
Digital Object Identifier: doi:10.1305/ndjfl/1054301354
Mathematical Reviews number (MathSciNet): MR1993389
Zentralblatt MATH identifier: 1023.03007

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Project Euclid: euclid.ndjfl/1040248461
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