Français
Real closed fields and models of Peano arithmetic
Multi angle
Authors : Kuhlmann, Salma (Author of the conference)
CIRM (Publisher )
06A05 - Total order
12J10 - Valued fields
12J15 - Ordered fields
12L12 - Model theory
13A18 - Valuations and their generalizations [See also 12J20]
CIRM (Publisher )
Loading the player...
|
Abstract :
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.
MSC Codes : 06A05 - Total order
12J10 - Valued fields
12J15 - Ordered fields
12L12 - Model theory
13A18 - Valuations and their generalizations [See also 12J20]
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 12/11/15 Conference Date : 13/10/15 Subseries : Research talks arXiv category : Logic ; Commutative Algebra Mathematical Area(s) : Algebra Format : MP4 (.mp4) - HD Video Time : 00:30:40 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-10-13_Kuhlmann.mp4 
|
Information on the Event
Event Title : Ordered algebraic structures and related topics / Structures algébriques ordonnées et leurs interactionsEvent Organizers : Broglia, Fabrizio ; Delon, Françoise ; Dickmann, Max ; Gondard, Danielle Dates : 12/10/15 - 16/10/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1155.html
Citation Data
DOI : 10.24350/CIRM.V.18863703Cite this video as: Kuhlmann, Salma (2015). Real closed fields and models of Peano arithmetic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18863703 URI : http://dx.doi.org/10.24350/CIRM.V.18863703 |
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.
- [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
