A valuation theoretic characterization of recursively saturated real closed fields. (English) Zbl 1372.03073
Summary: We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [F. V. Kuhlmann et al., J. Pure Appl. Algebra 169, No. 1, 71–90 (2002; Zbl 0998.12010)], where the authors gave such a characterization for \(\kappa\)-saturation, for a cardinal \(\kappa \geq \aleph _0\). Our result extends the characterization of Harnik and Ressayre for a divisible ordered abelian group to be recursively saturated.
MSC:
| 03C60 | Model-theoretic algebra |
| 12J20 | General valuation theory for fields |
| 03C57 | Computable structure theory, computable model theory |
| 12J15 | Ordered fields |
Keywords:
recursive saturation; Scott sets; natural valuation; value group; residue field; valuation rank; pseudo-Cauchy sequencesCitations:
Zbl 0998.12010References:
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