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Transactions of the American Mathematical Society

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Metric dimensions and tameness in expansions of the real field


Authors: Philipp Hieronymi and Chris Miller
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
Published electronically: October 18, 2019
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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
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: https://doi.org/10.1090/tran/7691
Keywords: Assouad dimension, topological dimension, expansion of the real field, projective hierarchy
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).
Article copyright: © Copyright 2019 American Mathematical Society