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A new Löwenheim-Skolem theorem

Authors: Matthew Foreman and Stevo Todorcevic
Journal: Trans. Amer. Math. Soc. 357 (2005), 1693-1715
MSC (2000): Primary 03C55
Published electronically: December 16, 2004
MathSciNet review: 2115072
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Abstract: This paper establishes a refinement of the classical Löwenheim-Skolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.

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Additional Information

Matthew Foreman
Affiliation: Department of Mathematics, University of California, Irvine, California 92697

Stevo Todorcevic
Affiliation: CNRS, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 05, Paris, France

Received by editor(s): June 26, 2002
Published electronically: December 16, 2004
Additional Notes: The first author was partially supported by NSF grant DMS-9803126 and the Equipe d’Analyse, Université Paris VI
Article copyright: © Copyright 2004 American Mathematical Society

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