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A valuation theoretic characterization of recursively saturated real closed fields

A valuation theoretic characterization of recursively saturated real closed fields

Type of Publication: Journal article
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-0-288863
Author: D'Aquino, Paola; Kuhlmann, Salma; Lange, Karen
Year of publication: 2015
Published in: The Journal of Symbolic Logic ; 80 (2015), 1. - pp. 194-206. - ISSN 0022-4812. - eISSN 1943-5886
DOI (citable link): https://dx.doi.org/10.1017/jsl.2014.21
Summary:
We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization for κ≥N0. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.
Subject (DDC): 510 Mathematics
Keywords: Recursive saturation, Scott sets, natural valuation, value group, residue field, valuation rank, pseudo-Cauchy sequences
Link to License: Terms of use
Bibliography of Konstanz: Yes
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D'AQUINO, Paola, Salma KUHLMANN, Karen LANGE, 2015. A valuation theoretic characterization of recursively saturated real closed fields. In: The Journal of Symbolic Logic. 80(1), pp. 194-206. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.1017/jsl.2014.21

@article{DAquino2015valua-31379, title={A valuation theoretic characterization of recursively saturated real closed fields}, year={2015}, doi={10.1017/jsl.2014.21}, number={1}, volume={80}, issn={0022-4812}, journal={The Journal of Symbolic Logic}, pages={194--206}, author={D'Aquino, Paola and Kuhlmann, Salma and Lange, Karen} }

Lange, Karen D'Aquino, Paola 2015 terms-of-use A valuation theoretic characterization of recursively saturated real closed fields Lange, Karen Kuhlmann, Salma D'Aquino, Paola 2015-07-07T13:56:51Z We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization for κ≥N<sub>0</sub>. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated. eng Kuhlmann, Salma 2015-07-07T13:56:51Z

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