On a theorem of Vaught for first order logic with finitely many variables

We prove that the existence of atomic models for countable atomic theories does not hold for L n the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that L n has been studied in recent times as a multi-modal logic with applicati...

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Bibliographic Details
Published inJournal of applied non-classical logics Vol. 19; no. 1; pp. 97 - 112
Main Author Ahmed, Tarek Sayed
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Group 01.01.2009
Taylor & Francis Ltd
Subjects
algebraic logic
games on graphs
Language
Logic
model theory
polyadic algebras
Variables
Vaught's theorem
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ISSN1166-3081
1958-5780
DOI10.3166/jancl.19.97-112

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Summary:We prove that the existence of atomic models for countable atomic theories does not hold for L n the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that L n has been studied in recent times as a multi-modal logic with applications in computer science. 2000 MATHEMATICS SUBJECT CLASSIFICATION. 03C07, 03G15.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1166-3081
1958-5780
DOI:10.3166/jancl.19.97-112