  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.
