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June 2020 Coarse dimension and definable sets in expansions of the ordered real vector space
Erik Walsberg
Illinois J. Math. 64(2): 141-149 (June 2020). DOI: 10.1215/00192082-8303453

Abstract

Let ER. Suppose there is an s>0 such that |{kZ,mkm1:[k,k+1]E}|ms for all sufficiently large mN. Then there is an nN and a linear T:RnR such that T(En) is dense. As a corollary, we show that if E is in addition nowhere dense, then (R,<,+,0,(xλx)λR,E) defines every bounded Borel subset of every Rn.

Citation

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Erik Walsberg. "Coarse dimension and definable sets in expansions of the ordered real vector space." Illinois J. Math. 64 (2) 141 - 149, June 2020. https://doi.org/10.1215/00192082-8303453

Information

Received: 19 March 2019; Revised: 12 November 2019; Published: June 2020
First available in Project Euclid: 1 May 2020

zbMATH: 07210953
MathSciNet: MR4092952
Digital Object Identifier: 10.1215/00192082-8303453

Subjects:
Primary: 03C64

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 2 • June 2020
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