Submission date: 29 March 2012.

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.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text arXiv 1203.6299: pdf, ps.