Model Theory Seminar

The seminar meets Tuesdays at 11:00 AM in 427 SEO. During the Fall 2016 semester, the seminar is thematic and the talks will be around valued fields.

The first three weeks of lecture will be aimed at understanding some basic notions around valuation theory.
The following four weeks will be aimed at proving elimination of imaginaries for algebraically closed valued fields.
Following this, other topics related to these will be investigated. Please take a look at the papers below so that you have some idea of topic you might be interested in the seminar looking into.

Date	Name	Title	Description
8/30	Marker	Basics of valued fields I	The talk will be a brief introduction to valued fields and some of the results that are needed to prove quantifier elimination. Notes
9/6	Freitag	Consequences of quantifier elimination	We will discuss some consequences of quantifier elimination.
9/13	Freitag/Marker	Basics of valued fields II: QE	The proof of QE for ACVF will be completed. Notes
9/20	Berner	Elimination of Imaginaries I	Berner covered the definable modules material.
9/27	Berner/Wolf	Elimination of Imaginaries II
10/4	No seminar
10/11	Wolf	Elimination of Imaginaries III	Wolf covered the generalities on the independence notions defined in section 2.
10/18	Freitag	Elimination of Imaginaries IV	Freitag covered an abstract criterion for EI and then started the coding of finite sets.
10/25	Freitag/Sluutsky	Elimination of Imaginaries IV

Material for first three weeks:

During the first three weeks, we are covering the basics of valuation theory. Marker's lectures will follow notes of van den Dries on valued fields. Notes on the notes:

The first three lectures are going to involve two things - understanding the basics of valuation theory and proving quantifier elimination (QE) for ACVF and understanding the consequences of QE.
In section 3 of the notes, van den Dries proves QE.
There are also nice notes on valued fields here and here.
Notes from which Dave Marker's lectures are based.

Material for four weeks of EI:

During these weeks we are going to following Will Johnson's paper.
Will's proof of EI is a simplication of a simplification of the original proof.

Comments on Will's paper and the talks:

Sections 1.3 and 1.4 of Will's paper (pg 3- pg 6), which would correspond roughly to lecture EI#1 does not require any model theory background besides a few small things.
Section 2 and section 3.1 (pg 6 - pg 11) of Will's paper requires the most model theory and would be most natural to do as one of the EI lectures. It could be done as EL#2 or it could be done later.
Sections 4 and 5 would be natural to group together as two lectures. Both of these talks require using notions from section 2.

We can talk about the order of the lectures if you think your background is not best matched for the current week assignments.

After the imaginaries are gone:

After the EI lectures, there are a variety of options, depending on interest and availability of speakers. Here is one suggestion for a further topic:

More elimination of imaginaries and applications