Let . Suppose there is an such that for all sufficiently large . Then there is an and a linear such that is dense. As a corollary, we show that if is in addition nowhere dense, then defines every bounded Borel subset of every .
"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