Transactions of the American Mathematical Society

Author(s): Matthew Foreman; Stevo Todorcevic
Journal: Trans. Amer. Math. Soc. 357 (2005), 1693-1715.
MSC (2000): Primary 03C55
Posted: December 16, 2004
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03C55

Matthew Foreman
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: mforeman@math.uci.edu

Stevo Todorcevic
Affiliation: CNRS, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 05, Paris, France
Email: stevo@logique.jussieu.fr

DOI: 10.1090/S0002-9947-04-03445-2
PII: S 0002-9947(04)03445-2
Received by editor(s): June 26, 2002
Posted: December 16, 2004
Additional Notes: The first author was partially supported by NSF grant DMS-9803126 and the Equipe d'Analyse, Université Paris VI
Copyright of article: Copyright 2004, American Mathematical Society

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