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

2018/11/22 by Figueiredo, Rodrigo, Mariano, Hugo Luiz
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1811.09255

Abstract

In the talk \citevandendries-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.

Related

• Tame structures and open cores
• Metric dimensions and tameness in expansions of the real field
• Expansions of the real field by open sets: definability versus interpretability
• Model theory of tame valued fields and beyond: recent developments and open questions
• Mini-Workshop: Topological and Differential Expansions of o-minimal Structures