We prove quantifier elimination for the field ℚp((tℚ)) (the completion of the field of Puiseux series over ℚp) 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 ℚp((tℚ)) is b-minimal in this language.
"p-adically closed fields with nonstandard analytic structure." J. Symbolic Logic 75 (3) 802 - 816, September 2010. https://doi.org/10.2178/jsl/1278682201