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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A dichotomy for expansions of the real field
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by Antongiulio Fornasiero, Philipp Hieronymi and Chris Miller PDF
Proc. Amer. Math. Soc. 141 (2013), 697-698 Request permission

Abstract:

A dichotomy for expansions of the real field is established: Either $\mathbb Z$ is definable or every nonempty bounded nowhere dense definable subset of $\mathbb R$ has Minkowski dimension zero.
References
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Additional Information
  • Antongiulio Fornasiero
  • Affiliation: Institut für Mathematische Logik, Einsteinstrasse 62, 48149 Münster, Germany
  • MR Author ID: 794986
  • Email: antongiulio.fornasiero@googlemail.com
  • Philipp Hieronymi
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
  • MR Author ID: 894309
  • Email: p@hieronymi.de
  • Chris Miller
  • Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
  • MR Author ID: 330760
  • Email: miller@math.osu.edu
  • Received by editor(s): May 13, 2011
  • Received by editor(s) in revised form: July 17, 2011
  • Published electronically: July 13, 2012
  • Additional Notes: The research of the third author was partly supported by NSF Grant DMS-1001176.
  • Communicated by: Julia Knight
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 697-698
  • MSC (2010): Primary 03C64; Secondary 28A75
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11369-3
  • MathSciNet review: 2996974