Quantifier elimination for quasi-real closed fields

Mickaël Matusinski; Simon Müller

doi:10.5802/crmath.169

Mathematical logic

Quantifier elimination for quasi-real closed fields

Mickaël Matusinski ¹; Simon Müller ²

¹ Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France
² Universität Konstanz, 78467 Konstanz, Germany

Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 291-295.

Abstract
Résumé

We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields and real closed valued fields.

Nous prouvons l’élimination des quantificateurs pour la théorie des corps quasi-réels clos munis d’une valuation compatible. Cela reprend et unifie les mêmes résultats connus pour les corps algébriquement clos et les corps réels clos.

Received: 2020-05-26
Accepted: 2020-12-13
Published online: 2021-04-20

DOI: 10.5802/crmath.169

Classification: 03C10, 03C64, 12J10, 12J15, 12L12

Author's affiliations:

Mickaël Matusinski ¹; Simon Müller ²

¹ Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France
² Universität Konstanz, 78467 Konstanz, Germany

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Quantifier elimination for quasi-real closed fields},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {291--295},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {3},
     year = {2021},
     doi = {10.5802/crmath.169},
     language = {en},
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Mickaël Matusinski; Simon Müller. Quantifier elimination for quasi-real closed fields. Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 291-295. doi : 10.5802/crmath.169. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.169/

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