A note on ℵα-saturated o-minimal expansions of real closed fields

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2016
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D'Aquino, Paola
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Algebra and Logic. 2016, 54(6), pp. 502-506. ISSN 0002-5232. eISSN 1573-8302. Available under: doi: 10.1007/s10469-016-9369-6
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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 ℵα-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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510 Mathematik
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ISO 690D'AQUINO, Paola, Salma KUHLMANN, 2016. A note on ℵα-saturated o-minimal expansions of real closed fields. In: Algebra and Logic. 2016, 54(6), pp. 502-506. ISSN 0002-5232. eISSN 1573-8302. Available under: doi: 10.1007/s10469-016-9369-6
BibTex
@article{DAquino2016satur-33138.2,
  year={2016},
  doi={10.1007/s10469-016-9369-6},
  title={A note on ℵ<sub>α</sub>-saturated o-minimal expansions of real closed fields},
  number={6},
  volume={54},
  issn={0002-5232},
  journal={Algebra and Logic},
  pages={502--506},
  author={D'Aquino, Paola and Kuhlmann, Salma}
}
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