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September 2012 Vaught's theorem on axiomatizability by a scheme
Albert Visser
Bull. Symbolic Logic 18(3): 382-402 (September 2012). DOI: 10.2178/bsl/1344861888

Abstract

In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 has decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles.

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Albert Visser. "Vaught's theorem on axiomatizability by a scheme." Bull. Symbolic Logic 18 (3) 382 - 402, September 2012. https://doi.org/10.2178/bsl/1344861888

Information

Published: September 2012
First available in Project Euclid: 13 August 2012

zbMATH: 1272.03063
MathSciNet: MR2987522
Digital Object Identifier: 10.2178/bsl/1344861888

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Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.18 • No. 3 • September 2012
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