Nov 8, 12:30–13:45

Tight stationarity and pcf theory  part one 
Bill Chen (BGU) 
I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcftheoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.

Nov 15, 12:30–13:45

Tight stationarity and pcf theory  part two 
Bill Chen (BGU) 
I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcftheoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.

Nov 22, 12:30–13:45

Pseudofinite groups and centralizers 
Daniel Palacín (HUJI) 
In this talk I will prove that any pseudofinite group contains an infinite abelian subgroup. Additionally, I shall also discuss some other results concerning pseudofinite groups and centralizers.
This is joint work with Nadja Hempel.

Nov 29, 12:30–13:45

Around the Small Index Property on quasiminimal classes 
Andrés Villaveces (Universidad Nacional, Bogotá) 
In the study of the connection between automorphism groups of models and the models themselves (or their theories, or their biinterpretability class), the Small Index Property (SIP) has played a central role. The work of Hodges, Lascar, Shelah and Rubin among others has established in many cases when a model of a first order theory T has the Small Index Property.
With Ghadernezhad, we have studied this property for more general homogeneous classes. We have isolated properties of closure notions that allow to prove the SIP for some nonelementary cases, including Zilber’s pseudoexponentiation and other examples.
I will present a panorama of these results, including our more recent generalizations of the LascarShelah proof of SIP for uncountable structures. This last part is joint work with Zaniar Ghadernezhad.

Dec 6, 12:30–13:45

Elementary topology via finite topological spaces 
Misha Gavrilovich 
We observe that several elementary definitions in pointset topology
can be reformulated in terms of finite topological spaces
and elementary category theory. This includes compactness
of Hausdorff spaces, being connected, discrete, the separation axioms.
Though elementary, these observations raise a few open questions.
For example, I was not able to prove that this reformulation of
compactness gives the correct answer for nonHausdorff spaces,
or whether implications between various topological properties
can also be proved entirely in terms of finite topological spaces,
without any additional axioms.

Dec 13

Structural approximation 
Boris Zilber (Oxford) 
In the framework of positive model theory I will give (recall) a definition of ``structural approximation’’ which is used in my paper on modeltheoretic interpretation of quantum mechanics. I will then present some general theory as well as a few examples, if time permits.

Dec 20

Induced Ramsey Theory in inverse limits 
Menachem Kojman (BGU) 
For every finite ordered graph $H$ there is a natural number $k(H)>1$ such that whenever all copies of $H$ in the ordered inverse limit of all finite ordered graphs are partitions to finitely many Borel parts, then there is a (closed) copy of the inverse limit graph in itself whose copies of $H$ meet at most $k(H)$ many parts.
The probability that a random ordered graph on $n$ vertices satisfies $k(H)=1$ tends to 1 as $n$ grows.
Joint work with S. Geschke and S. Huber.

Jan 3

The BaerKrull Theorem for Quasiordered fields 
Salma Kuhlmann (Konstanz) 
In my seminar talk on 29.12.2015, I introduced the notion of quasiordered fields, proved Fakhruddin’s dichotomy. In this talk, I will present a version of a classical theorem in real algebra (the BaerKrull theorem) for quasiordered fields.

Jan 17

A theory of pairs for weakly ominimal nonvaluational structures 
Assaf Hasson (BGU) 
A linearly ordered structure is weakly ominimal if every definable set is a finite boolean combination of convex sets. A weakly ominimal expansion of an ordered group is nonvaluational if it admits no nontrivial definable convex subgroups. By a theorem of BaizalovPoizat if M is an ominimal expansion of a group and N is a dense elementary substructure then the structure induced on N by all Mdefinable sets is weakly ominimal nonvaluational.
It is natural to ask whether all nonvaluational structures are obtained in this way. We will give examples showing that this is not the case. We will show, however, that if M is nonvaluational then there exists M^, an ominimal structure embedding M densely (as an ordered set) such that M (as a pure set) extended by all M^definable sets is precisely the structrue M. We will give a complete axiomatisation of the theory of the pair (M^,M), show that it depends only on the theory of M, and that it shares many common features with the theory of dense ominimal pairs. In particular (M^,M) has dense open core (i.e., the reduct consisting only of definable open sets is ominimal).
Based on joint work with E. BarYehuda and Y. Peterzil.
