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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Cofinality spectrum theorems in model theory, set theory, and general topology
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by M. Malliaris and S. Shelah
J. Amer. Math. Soc. 29 (2016), 237-297
Published electronically: April 9, 2015


We connect and solve two long-standing open problems in quite different areas: the model-theoretic question of whether $SOP_2$ is maximal in Keisler’s order, and the question from general topology/set theory of whether $\mathfrak {p} = \mathfrak {t}$, the oldest problem on cardinal invariants of the continuum. We do so by showing these problems can be translated into instances of a more fundamental problem which we state and solve completely, using model-theoretic methods.
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Bibliographic Information
  • M. Malliaris
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
  • MR Author ID: 864805
  • Email:
  • S. Shelah
  • Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, TheHebrew University of Jerusalem, Jerusalem, 91904, Israel, and Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of NewJersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
  • MR Author ID: 160185
  • ORCID: 0000-0003-0462-3152
  • Email:
  • Received by editor(s): August 27, 2012
  • Received by editor(s) in revised form: January 14, 2014, and January 11, 2015
  • Published electronically: April 9, 2015
  • Additional Notes: The first author was partially supported by NSF grant DMS-1001666, by Shelah’s NSF grant DMS-1101597, by a Gödel research fellowship, and by a Sloan fellowship.
    The second author was partially supported by the Israel Science Foundation grants 710/07 and 1053/11. This is paper 998 in Shelah’s list of publications.
  • © Copyright 2015 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 29 (2016), 237-297
  • MSC (2010): Primary 03C20, 03C45, 03E17; Secondary 03E05
  • DOI:
  • MathSciNet review: 3402699