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

00:00:00 / 00:00:00

Real closed fields and models of Peano arithmetic

By Salma Kuhlmann

Appears in 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.

Information about the video

Date of recording 13/10/2015
Date of publication 12/11/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18863703
Cite this video 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

Domain(s)

Bibliography

[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

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2025

Give feedback