Remarks on expansions of the real field: tameness, Hardy fields and smooth rings

Abstract

In the talk \cite{vandendries-matthias-} presented at Logic and Foundations section of ICM-2018, Rio de Janeiro, the authors analyze, under a model-theoretic perspective, three ways to enrich the real continuum by infinitesimal and infinite quantities. In the present work, we present a first model-theoretic connection of another (but related to the previous one) triple of structures: o-minimal structures, Hardy fields and smooth rings.

10 pages