English

Interpreting the projective hierarchy in expansions of the real line

Logic 2015-10-13 v3

Abstract

We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number a, the expansion of the ordered Q(a)-vector space of real numbers by the set of natural numbers defines multiplication on the real numbers.

Keywords

Cite

@article{arxiv.1203.6299,
  title  = {Interpreting the projective hierarchy in expansions of the real line},
  author = {Philipp Hieronymi and Michael Tychonievich},
  journal= {arXiv preprint arXiv:1203.6299},
  year   = {2015}
}