A P-adic structure which does not interpret an infinite field but whose Shelah completion does

Abstract

We give a $p$-adic example of a structure whose Shelah completion interprets ${\mathbb{Q}}_p$ but which does not (provided an extremely plausible conjecture holds) interpret an infinite field. In the final section we discuss the significance of such examples for a possible future geometric theory of $\mathrm{NIP}$ structures.

References in corpus (1)

• An NIP structure which does not interpret an infinite group but whose Shelah expansion interprets an infinite field