Bulletin of Symbolic Logic

Vaught's theorem on axiomatizability by a scheme

Albert Visser

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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.

Article information

Source
Bull. Symbolic Logic Volume 18, Issue 3 (2012), 382-402.

Dates
First available in Project Euclid: 13 August 2012

Permanent link to this document
http://projecteuclid.org/euclid.bsl/1344861888

Digital Object Identifier
doi:10.2178/bsl/1344861888

Zentralblatt MATH identifier
06083933

Mathematical Reviews number (MathSciNet)
MR2987522

Subjects
Primary: 03B10, 03B30, 03F25

Keywords
predicate logic axiom scheme

Citation

Visser, Albert. Vaught's theorem on axiomatizability by a scheme. Bulletin of Symbolic Logic 18 (2012), no. 3, 382--402. doi:10.2178/bsl/1344861888. http://projecteuclid.org/euclid.bsl/1344861888.


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