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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Metric dimensions and tameness in expansions of the real field
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by Philipp Hieronymi and Chris Miller PDF
Trans. Amer. Math. Soc. 373 (2020), 849-874 Request permission

Abstract:

For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.
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Additional Information
  • 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): June 11, 2017
  • Received by editor(s) in revised form: August 30, 2018
  • Published electronically: October 18, 2019
  • Additional Notes: This work was partially supported by NSF grant DMS-1300402 and UIUC Campus Research Board awards 13086 and 14194 (first author) and NSF grant DMS-1001176 (second author).
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 849-874
  • MSC (2010): Primary 03C64; Secondary 03E15, 28A05, 28A75, 54F45, 54H05
  • DOI: https://doi.org/10.1090/tran/7691
  • MathSciNet review: 4068252