Submission date: 23 February 2015.

Abstract:

We introduce the notion of R-analytic functions. These are definable in an o-minimal expansion of a real closed field R and are locally the restriction of a K-differentiable function (defined by Peterzil and Starchenko) where K=R[\sqrt{-1}] is the algebraic closure of R. The class of these functions in this general setting exhibits the nice properties of real analytic functions. We also define strongly R-analytic functions. These are globally the restriction of a K-differentiable function. We show that in arbitrary models of important o-minimal theories strongly R-analytic functions abound and that the concept of analytic cell decomposition can be transferred to non-standard models.

Mathematics Subject Classification: 03C64, 14P20, 26E05, 32B05, 32B20

Keywords and phrases:

Full text arXiv 1502.06436: pdf, ps.