Illinois Journal of Mathematics

Coarse dimension and definable sets in expansions of the ordered real vector space

Erik Walsberg

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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.

Article information

Illinois J. Math., Volume 64, Number 2 (2020), 141-149.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality


Walsberg, Erik. Coarse dimension and definable sets in expansions of the ordered real vector space. Illinois J. Math. 64 (2020), no. 2, 141--149. doi:10.1215/00192082-8303453.

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