A note on $\aleph_α$-saturated o-minimal expansions of real closed fields

Paola D'Aquino; Salma Kuhlmann

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arXiv · 1112.4078

A note on $\aleph_α$-saturated o-minimal expansions of real closed fields

Paola D'Aquino·Salma Kuhlmann

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Abstract

We give necessary and sufficient conditions for a polynomially bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be $\aleph_α$-saturated. The conditions are in terms of the value group, residue field, and pseudo- Cauchy sequences of the natural valuation on the real closed field. This is achieved by an analysis of types, leading to the trichotomy. Our characterization provides a construction method for saturated models, using fields of generalized power series.

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Paola D'Aquino, Salma Kuhlmann. 2015-10-23. A note on $\aleph_α$-saturated o-minimal expansions of real closed fields. https://arxiv.org/abs/1112.4078

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