Abstract

We prove quantifier elimination for the field ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ (the completion of the field of Puiseux series over ${\Bbb Q}_{p}$ ) 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 ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ is b-minimal in this language.