Expansions of subfields of the real field by a discrete set
Logic
2011-12-23 v4
Abstract
Let K be a subfield of the real field, D be a discrete subset of K and f : D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines the set of integers. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines the set of integers. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire Category Theorem.
Keywords
Cite
@article{arxiv.1012.3508,
title = {Expansions of subfields of the real field by a discrete set},
author = {Philipp Hieronymi},
journal= {arXiv preprint arXiv:1012.3508},
year = {2011}
}