@article{21a7376932ac46c8b23a0a3c82afe74c,
title = "Metric dimensions and tameness in expansions of the real field",
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.",
keywords = "Assouad dimension, Expansion of the real field, Projective hierarchy, Topological dimension",
author = "Philipp Hieronymi and Chris Miller",
note = "Funding Information: Received by the editors June 11, 2017, and, in revised form, August 30, 2018. 2010 Mathematics Subject Classification. Primary 03C64; Secondary 03E15, 28A05, 28A75, 54F45, 54H05. Key words and phrases. Assouad dimension, topological dimension, expansion of the real field, projective hierarchy. 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).",
year = "2020",
doi = "10.1090/tran/7691",
language = "English (US)",
volume = "373",
pages = "849--874",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "2",
}