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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A dichotomy for expansions of the real field


Authors: Antongiulio Fornasiero, Philipp Hieronymi and Chris Miller
Journal: Proc. Amer. Math. Soc. 141 (2013), 697-698
MSC (2010): Primary 03C64; Secondary 28A75
Published electronically: July 13, 2012
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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.


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Additional Information

Antongiulio Fornasiero
Affiliation: Institut für Mathematische Logik, Einsteinstrasse 62, 48149 Münster, Germany
Email: antongiulio.fornasiero@googlemail.com

Philipp Hieronymi
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Email: p@hieronymi.de

Chris Miller
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
Email: miller@math.osu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11369-3
PII: S 0002-9939(2012)11369-3
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.