p-adically closed fields with nonstandard analytic structure

Abstract

We prove quantifier elimination for the field ℚ_p((t^ℚ)) (the completion of the field of Puiseux series over ℚ_p) in Macintyre's language together with symbols for functions in a class containing both t-adically and p-adically overconvergent functions. We also show that the theory of ℚ_p((t^ℚ)) is b-minimal in this language.