A new Löwenheim-Skolem theorem
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- by Matthew Foreman and Stevo Todorcevic PDF
- Trans. Amer. Math. Soc. 357 (2005), 1693-1715 Request permission
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.References
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Additional Information
- Matthew Foreman
- Affiliation: Department of Mathematics, University of California, Irvine, California 92697
- MR Author ID: 194940
- Email: mforeman@math.uci.edu
- Stevo Todorcevic
- Affiliation: CNRS, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 05, Paris, France
- MR Author ID: 172980
- Email: stevo@logique.jussieu.fr
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 1693-1715
- MSC (2000): Primary 03C55
- DOI: https://doi.org/10.1090/S0002-9947-04-03445-2
- MathSciNet review: 2115072