Submission date: 22 November 2018

Abstract:

In the talk presented at Logic and Foundations section of ICM-2018, Rio de Janeiro, the authors (Aschenbrenner, Van den Dries and Van der Hoeven) 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.

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Full text arXiv 1811.09255: pdf, ps.