On arc-analytic functions definable by a Weierstrass system

Abstract

This paper presents certain characterizations through blowing up of arc-analytic functions definable by a convergent Weierstrass system closed under complexification. Consider a real convergent Weierstrass system W closed under complexification and the o-minimal expansion R of the real field by restricted Wanalytic functions. Our previous article [6] presented several theorems about the rectilinearization of W-subanalytic functions and their application to quantifier elimination for the structure R. In this paper, we shall apply those results to the theory of arc-W-analytic functions definable in the structure R. In the sequel, the word "definable" will mean "definable in the structure R".