Metric dimensions and tameness in expansions of the real field

math.LO

/ Authors

/ 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.

Metric dimensions and tameness in expansions of the real field

math.LO

/ Authors

Philipp Hieronymi, Chris Miller

/ 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.