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_{\alpha}-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.
A NOTE ON $\aleph_{\alpha}$-SATURATED o-MINIMAL EXPANSIONS OF REAL CLOSED FIELDS
D'AQUINO, Paola;
2016
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_{\alpha}-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.File in questo prodotto:
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