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2010 Abstract Elementary Classes with Löwenheim-Skolem Number Cofinal with ω
Gregory M. Johnson
Notre Dame J. Formal Logic 51(3): 361-371 (2010). DOI: 10.1215/00294527-2010-022

Abstract

In this paper we study abstract elementary classes with Löwenheim-Skolem number κ , where κ is cofinal with ω , which have finite character. We generalize results obtained by Kueker for κ = ω . In particular, we show that K is closed under L , κ -elementary equivalence and obtain sufficient conditions for K to be L , κ -axiomatizable. In addition, we provide an example to illustrate that if κ is uncountable regular then K is not closed under L , κ -elementary equivalence.

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Gregory M. Johnson. "Abstract Elementary Classes with Löwenheim-Skolem Number Cofinal with ω." Notre Dame J. Formal Logic 51 (3) 361 - 371, 2010. https://doi.org/10.1215/00294527-2010-022

Information

Published: 2010
First available in Project Euclid: 18 August 2010

zbMATH: 1207.03040
MathSciNet: MR2675688
Digital Object Identifier: 10.1215/00294527-2010-022

Subjects:
Primary: 03C48
Secondary: 03C75

Keywords: abstract elementary class , finite character , Infinitary logic

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 3 • 2010
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