Die folgenden Vorträge haben im Sommersemester 2013 im Oberseminar Modelltheorie stattgefunden.

 

Montag, 15.04.2013 um 15.15 Uhr, Oberseminar Modelltheorie

kein Vortrag

 

Montag, 22.04.2013 um 15.15 Uhr, Oberseminar Modelltheorie

kein Vortrag

 

Montag, 29.04.2013 um 15.15 Uhr, Oberseminar Modelltheorie

kein Vortrag

 

Montag, 06.05.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Artem Chernikov (Hebrew University of Jerusalem)

(Gast von Salma Kuhlmann)

Fields with NTP2

Abstract: NTP2 is a large class of first-order theories introduced by Shelah and generalising both simple and NIP theories. It provides a natural setting for the theory of forking beyond simplicity, and also contains new important algebraic examples: any ultraproduct of p-adics viewed as a valued field is NTP2, as well as certain valued difference fields. But what can be said about groups and fields definable in NTP2 structures? One result is that every field definable in an NTP2 structure has only finitely many Artin-Schreier extensions. In this talk I will give a survey of the area and my recent work with Martin Hils, Itay Kaplan and Pierre Simon.

 

Montag, 13.05.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Krzysztof Krupinski (Uniwersytetu Wrocławskiego, Poland)

(Gast von Salma Kuhlmann)

On superrosy fields

Abstract: There is a long history of results describing the structure of fields under various model-theoretic assumptions. One of the fundamental theorems says that each superstable field is algebraically closed. There are two important conjectures generalizing this theorem: the first one predicts that each supersimple field is pseudo algebraically closed, the second one says that each superrosy field with NIP is either algebraically or real closed. I will discuss certain partial results around the second conjecture. In particular, I will formulate a weaker conjecture that whenever we have a non-trivial valuation on a superrosy field with NIP, then the value group is divisible and the residue field is either algebraically or real closed. I will discuss how to prove this conjecture in the positive characteristic case and what is left for the zero characteristic case.

 

Montag, 20.05.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Feiertag, kein Vortrag

 

Montag, 27.05.2013 um 15.15 Uhr, Oberseminar Modelltheorie

kein Vortrag

 

Montag, 03.06.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Pantelis E. Eleftheriou (University of Waterloo, Canada)

(Gast von Salma Kuhlmann)

Pregeometries and definable groups

Abstract: We describe a recent program for analyzing definable sets and groups in certain model theoretic settings. Those settings include:
(a) o-minimal structures (M, P), where M is an ordered group and P is a real closed field defined on a bounded interval (joint work with Peterzil),
(b) tame expansions (M, P) of a real closed field M by a predicate P, such as expansions with o-minimal open core (work in progress with Gunaydin).
The analysis first goes through a local level, where a pertinent notion of a pregeometry and generic elements is each time introduced.

 

Montag, 10.06.2013 um 15.15 Uhr, Oberseminar Modelltheorie

kein Vortrag

 

Montag, 17.06.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Will Anscombe (University of Oxford)

(Gast von Salma Kuhlmann)

Definability in fields of power series via an improved Hensel-like Lemma

Abstract: We detail our Hensel-like Lemma in its original form, its application to the study of definability in power series fields, and then give an indication of present efforts to improve the lemma to reveal more detail about existentially definable sets.

 

Montag, 24.06.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Nikesh Solanki (Manchester)

(Gast von Arno Fehm)

Uniform Companions For Differential Field Expansions in Characteristic 0

Abstract: In 2005 M. Tressl presented a theory UC of differential fields in several commuting derivatives of characteristic zero, which serves as a model companion for every theory of differential fields extending a model complete theory in the language of rings whose models are large as pure fields. We call UC a "uniform companion" of theories of large fields in the language rings. In this talk I will show that methods of M. Tressl can be generalised so as to obtain uniform companions for theories in any relational expansion of the language of rings whose models obey a generalised notion of largeness for relational field expansions. This generalised notion of largeness also takes into account the relations satisfied by the rational points, which I shall of course explain explicitly. I will also present some interesting examples where these new uniform companion can be applied to obtain new model companions, in particular, to the case of fields with pseudovaluation rings.

 

Dienstag, 02.07.2013 um 13.30 Uhr, Oberseminar Modelltheorie

Franziska Jahnke (Universität Münster)

(Gast von Arno Fehm)

Definable henselian valuations

Abstract: A non-trivial henselian valuation on a field K is often so intrinsic to K that it is already definable in the language of rings. However, by the work of Prestel and Ziegler, there are henselian valued fields which are neither separably nor real closed and which do not admit any non-trivial 0-definable valuation. In this talk, we will give a range of criteria which ensure the existence of a 0-definable henselian valuation on a henselian field. We will discuss work towards a complete classification of those fields in the residue characteristic 0 case.

 

Montag, 08.07.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Katharina Dupont (Konstanz)

Applying Keisler Measures on the Axioms of Valuation Topologies

Abstract: For my PhD project I am working on the question "Under which conditions does a dependent field admit a non-trivial definable valuation?".

In his preprint "Definable Valuations" Koenigsmann defines for a subgroup G of a field K the valuation ring O_G.

Assume q ≠ char(K) prime such that G:=(K\{0})^q ≠ K\{0}. Then O_G is (topologically equivalent to) a non-trivial definable valuation ring if and only if the set B_G:={\bigcap_{i=1}^n a_i(G+1) | n ∈ \N, a_i ∈ K\{0}} fulfills the six axioms (V 1)-(V 6) of V-topologies, i.e. B_G is a basis of zero neighbourhoods of a topology induced by an absolute value or a valuation.

Recently we have been able to approach these axioms (for a dependent field K satisfying [K\{0}:(K\{0})^q]

 

Montag, 15.07.2013 um 15.15 Uhr, Oberseminar Modelltheorie

Quentin Brouette (Universite de Mons, Belgique)

(Gast von Salma Kuhlmann)

Abstract: We will consider formally real differential fields extensions and their differential Galois groups (that is the group of automorphisms of L in the language {+,-,.,^{-1},',0,1} and fixing K).