A valuation theoretic characterization of recursively saturated real closed fields

D'Aquino, Paola; Kuhlmann, Salma; Lange, Karen

doi:10.1017/jsl.2014.21

A valuation theoretic characterization of recursively saturated real closed fields

Publikationstyp:	Zeitschriftenartikel
URI (zitierfähiger Link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-0-288863
Autor/innen:	D'Aquino, Paola; Kuhlmann, Salma; Lange, Karen
Erscheinungsjahr:	2015
Erschienen in:	The Journal of Symbolic Logic ; 80 (2015), 1. - S. 194-206. - ISSN 0022-4812. - eISSN 1943-5886
DOI (zitierfähiger Link):	https://dx.doi.org/10.1017/jsl.2014.21
Zusammenfassung:	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.
Fachgebiet (DDC):	510 Mathematik
Schlagwörter:	Recursive saturation, Scott sets, natural valuation, value group, residue field, valuation rank, pseudo-Cauchy sequences
Link zur Lizenz:	Deposit-Lizenz
Universitätsbibliographie:	Ja
Dieser Beitrag ist im Zusammenhang des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

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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 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