o-minimal expansions of real closed fields and completeness in the sense of Scott

Olivier Frécon (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

We consider an o-minimal expansion M=(R,<,+,...) of a real closed field, and a real closed field S, complete in the sense of D. Scott, containing R as a dense subfield. We show that M has an elementary extension N=(S,<,+,...) with domain S. Moreover, such a structure N with domain S is unique.

Mots clés: Real closed field; o-minimal structure

Domaines: Logique [math.LO]

Olivier Frécon. o-minimal expansions of real closed fields and completeness in the sense of Scott. 2015. ⟨hal-03704341⟩