The Decidability of the Class and the Axiom of Foundation

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Notre Dame Journal of Formal Logic 42 (1):41-53 (2001)
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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

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10.1305/ndjfl/1054301354

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