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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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