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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The stable regularity lemma revisited
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by Maryanthe Malliaris and Anand Pillay
Proc. Amer. Math. Soc. 144 (2016), 1761-1765
DOI: https://doi.org/10.1090/proc/12870
Published electronically: September 9, 2015

Abstract:

We prove a regularity lemma with respect to arbitrary Keisler measures $\mu$ on $V$, $\nu$ on $W$ where the bipartite graph $(V,W,R)$ is definable in a saturated structure ${\bar M}$ and the formula $R(x,y)$ is stable. The proof is rather quick, making use of local stability theory. The special case where $(V,W,R)$ is pseudofinite, $\mu$, $\nu$ are the counting measures, and ${\bar M}$ is suitably chosen (for example a nonstandard model of set theory), yields the stable regularity theorem of a work by the first author and S. Shelah, though without explicit bounds or equitability.
References
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Bibliographic Information
  • Maryanthe Malliaris
  • Affiliation: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
  • MR Author ID: 864805
  • Email: mem@math.uchicago.edu
  • Anand Pillay
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 139610
  • Email: apilla@nd.edu
  • Received by editor(s): May 1, 2015
  • Published electronically: September 9, 2015
  • Additional Notes: The first author was partially supported by NSF grant DMS-1300634 and a Sloan fellowship
    The second author was partially supported by NSF grant DMS-1360702
  • Communicated by: Mirna Džamonja
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 1761-1765
  • MSC (2010): Primary 03C45, 03C98, 05C75
  • DOI: https://doi.org/10.1090/proc/12870
  • MathSciNet review: 3451251