Real closed fields and models of Peano arithmetic | Vidéo | Carmin.tv

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Real closed fields and models of Peano arithmetic

De Salma Kuhlmann

Apparaît dans les collections : Ordered algebraic structures and related topics / Structures algébriques ordonnées et leurs interactions, Exposés de recherche

We say that a real closed field is an IPA-real closed field if it admits an integer part (IP) which is a model of Peano Arithmetic (PA). In [2] we prove that the value group of an IPA-real closed field must satisfy very restrictive conditions (i.e. must be an exponential group in the residue field, in the sense of [4]). Combined with the main result of [1] on recursively saturated real closed fields, we obtain a valuation theoretic characterization of countable IPA-real closed fields. Expanding on [3], we conclude the talk by considering recursively saturated o-minimal expansions of real closed fields and their IPs.

Informations sur la vidéo

Date de captation 13/10/2015
Date de publication 12/11/2015
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18863703
Citer cette vidéo Kuhlmann, Salma (13/10/2015). Real closed fields and models of Peano arithmetic. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18863703
URL https://dx.doi.org/10.24350/CIRM.V.18863703

Domaine(s)

Bibliographie

[1] D'Aquino, P., Kuhlmann, S., & Lange, K. (2015). A valuation theoretic characterization of recursively saturated real closed fields. Journal of Symbolic Logic, 80(1), 194-206 - http://dx.doi.org/10.1017/jsl.2014.21
[2] Carl, M., D'Aquino, P., Kuhlmann, S. (2014). Value groups of real closed fields and fragments of Peano Arithmetic. <arXiv:1205.2254> - http://arxiv.org/abs/1205.2254
[3] D'Aquino, P., Kuhlmann, S. (2015). $\kappa$-saturated o-minimal expansions of real closed fields. To appear in Algebra and Logic, 54(5)
[4] Kuhlmann, S. (2000). Ordered exponential fields. Providence, RI: American Mathematical Society. (Fields Institute Monograph Series, 12) - http://www.ams.org/bookstore-getitem?item=FIM-12

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