# Salma Kuhlmann: On the value group of a model of Peano arithmetic

Set Theory and Topology seminar (BGU)

On Wednesday, December 31, 16:45-18:30 (refreshments will be served from 16:35)
Place: Seminar room -101 in the Math building 58
Speaker: Salma Kuhlmann (Konstanz)
Title: On the value group of a model of Peano arithmetic
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.
References:
[1] D’Aquino, P. – Kuhlmann, S. – Lange, K. : A valuation theoretic characterization of recursively saturated real closed fields, to appear in the Journal of Symbolic Logic, arXiv: 1212.6842
[2] Carl, M. – D’Aquino, P. – Kuhlmann, S. : Value groups of real closed fields and fragments of Peano Arithmetic, arXiv: 1205.2254, submitted (2014)
[3] Conversano, A. – D’Aquino, P. – Kuhlmann, S : $\kappa$-Saturated o-minimal expansions of real closed fields, arXiv: 1112.4078 (2012)
[4] Kuhlmann, S. :Ordered Exponential Fields, The Fields Institute Monograph Series, vol 12. Amer. Math. Soc. (2000)