MidWest Model Theory Day
Tuesday, October 22, 2013 at UIC
Speakers: Vincent Guingona, Bradd Hart, Salma Kuhlmann
All talks are about an hour long, in SEO 636.
There will also be coffee&cookies in 636.
- 11am: Meet on the first floor of SEO if you're already here. We will leave to lunch at 11:20.
- 11:30am: Lunch at Joy Yee's
- 1pm: One talk
- 2:30: Two talk
- 4pm: Three talk
- 5:30pm: Dinner at Jaks Tap
It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.
Let us know (@math.wisc.edu">andrewsmath.wisc.edu) if you are planning to come to lunch and/or dinner so we can make approximately correct reservations!
Titles & Abstracts:
Title: On VC-minimal fields.
Abstract: I discuss recent work on classifying VC-minimal algebraic structures. The work began with J. Flenner and myself when we showed that an ordered group in the pure ordered group language is VC-minimal if and only if it is abelian and divisible. In that same paper, we classified VC-minimal abelian groups and showed that a quasi-VC-minimal Henselian valued field has a divisible value group. In recent work, I have applied our machinery toward classifying VC-minimal fields. I show that a VC-minimal ordered field is real closed and a VC-minimal stable field is algebraically closed. Moreover, I show that we can weaken the condition of VC-minimality to something I call dp-smallness, which sits strictly between VC-minimality and dp-minimality, and still maintain all of these classification results.
Title: Real Closed Fields and Models 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  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 ).
Combined with the main result of  on recursively saturated real
closed fields, we obtain a valuation theoretic characterization of
countable IPA-real closed fields. Expanding on , we
conclude the talk by considering recursively saturated o-minimal
expansions of real closed fields and their IPs.
 D'Aquino, P. - Kuhlmann, S. - Lange, K.:
A valuation theoretic characterization of recursively saturated
real closed fields, arXiv: 1212.6842 (2013)
 Carl, M. -
D'Aquino, P. - Kuhlmann, S.$\,$: Value groups of real closed
fields and fragments of Peano Arithmetic, arXiv: 1205.2254 (2012)
 Conversano, A. - D'Aquino, P. - Kuhlmann, S$\,$:
$\kappa$-Saturated o-minimal expansions of real closed fields,
arXiv: 1112.4078 (2012)
 Kuhlmann, S.$\,$: Ordered
Exponential Fields, The Fields Institute Monograph Series, vol 12.
Amer. Math. Soc. (2000)
Title:Revisiting classification theory from the 1970s
Abstract:In joint work with Ilijas Farah, Leonel Robert and Aaron Tikuisis, we have tried to understand the model theory involved in the classification problem of nuclear $C^*$-algebras. One of the original results in this area is a result of Elliott's that shows that any separable inductive limit of finite dimensional $C^*$-algebra $A$ is characterized by its dimension group, $K_0(A)$. I will outline a proof of this theorem in order to highlight the implicit model theory and to give several generalizations.
April 5th, 2016
October 28th, 2014
October 22nd, 2013
April 18th, 2013
October 23rd, 2012
April 26th, 2012
October 11th, 2011
April 7th, 2011
October 26th, 2010