Submission date: 4 October 2015.

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.

Mathematics Subject Classification: Primary 03C64, Secondary 03E15, 28A05, 28A75, 54F45, 54H05

Keywords and phrases:

Full text arXiv 1510.00964: pdf, ps.