**Welcome to the homepage of the Model Theory +972 - seminar, the common seminar between Ben Gurion University of the Negev, Hebrew University of Jerusalem and University of Haifa. This seminar aims to connect the researchers which share a common interest in model theory as well as the country code +972 in monthly meetings.**

**Upcoming Meeting**

**Upcoming Meeting**

**10.07.2019 - Hebrew University of Jerusalem**

**10.07.2019 - Hebrew University of Jerusalem**

**Place**Ross Building, Room 70

__11:00 Maryanthe Malliaris__

**Model Theory and Ultraproducts**

The talk will be about https://arxiv.org/abs/1906.10241 .

__14:30 Esther Elbaz__

**Structures with Finite Grothendieck Ring**

The Grothendieck rings have been introduced into model theory in the 2000's by Thomas Scanlon and Jan Krajicek on the one hand and François Loeser and Jan Denef on the other hand.

A natural generalization of the notion already known in algebraic geometry, they are obtained by identifying definable sets that are in definable bijection. The two laws of the rings rely on the disjoint union and the cartesian product.

A natural question that arises is to ask which ring can be obtained as the Grothendieck ring of a structure. In particular, it was an open question whether there exists a Grothendieck ring of finite characteristic and an afortiori finite Grothendieck ring.

In this talk, I will construct, for every positive integer n, a structure whose Grothendieck ring is Z/nZ. To do so, I will use ideas that can be adapted to construct, more generally, structures whose Grothendieck ring is a quotient of a polynomial ring over Z.

**Past Meetings****09.12.2018 - Hebrew University of Jerusalem**

**09.12.2018 - Hebrew University of Jerusalem**

**Place**Ross Building, Room 63

__10:00 Chloé Perin__

**Shelah rank of the free group**

tba

__14:00 Kobi Peterzil__

**An o-minimalist viewpoint of the group configuration**

Model theorists often ask those who work on o-minimal structures whether Hrushovski's group configuration has a meaning in that setting. In this talk I will review the classical notion of a group configuration and, if time permits, demonstrate how its o-minimal version helps proving a variant of a theorem by Elekes and Szabo, in the o-minimal setting, This last result, which is of combinatorial nature, is part of a joint work with Chernikov and Starchenko .

**03.07.2018 - Weizmann Institute of Science, Rehovot**

**03.07.2018 - Weizmann Institute of Science, Rehovot**

__10:00 Moshe Kamensky__

(10:00-10:45 Introduction into Finite Schemes, 11:15-12:30 Algebraic Geometry Seminar)

**Fields with free operators in positive characteristic**

Moosa and Scanlon defined a general notion of ``fields with operators'', that generalises those of difference and differential fields. In the case of ``free'' operators in characteristic zero they also analysed the basic model-theoretic properties of the theory of such fields. In particular, they showed in this case the existence of the model companion, a construction analogous to that of algebraically closed fields for usual fields. In positive characteristic, they provided an example showing that the model companion need not exist.

I will discuss work, joint with Beyarslan, Hoffman and Kowalski, that completes the description of the free case, namely, it provides a full classification of those free operators for which the model companion exists. Though the motivating question is model theoretic, the description and the proof are completely algebraic and geometric. If time permits, I will discuss additional properties, such as quantifier elimination. All notions related to model theory and to fields with operators will be explained (at least heuristically).

__14:00 Nick Ramsey__

**Classification Theory and the Construction of PAC Fields**

A field K is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety defined over K has a K-rational point. These fields were introduced by Ax in his characterization of pseudo-finite fields and have since become an important object of model-theoretic study. A remarkable theorem of Chatzidakis proves that, in a precise sense, independent amalgamation in a PAC field is controlled by independent amalgamation in the absolute Galois group. We will describe how this theorem and a graph-coding construction of Cherlin, van den Dries, and Macintyre may be combined to construct PAC fields with prescribed model-theoretic properties.

**03.06.2018 - Hebrew University of Jerusalem**

**03.06.2018 - Hebrew University of Jerusalem**

**Room 63 in the Ross Building, Giv'at Ram**

__Place__

__10:00 Yatir Halevi__

**On and around a generalization of von Staudt's theorem on cross-ratios**

__14:00 Daniel Palacín__

**Definable compactifications of ultraproducts and product-free sets**

Babai and Sós asked whether there exists a constant c>0 such that every finite group of order n has a product-free subset of size at least cn: that is, a subset X that does not contain three elements x, y and z with xy = z. Gowers proved that the answer is no. In this talk I will give a model-theoretic interpretation of the existence of a large product-free set in terms of definable compactifications of ultraproducts, obtaining an alternative proof of the aforementioned result of Gowers.

**06.05. 2018 - University of Haifa**

**06.05. 2018 - University of Haifa**

**Place**Room 570, in the Education and Science building (or complex), across from the Eshkol Tower, near the first bus stop, as you enter the campus from Haifa.

__Tomasz Rzepecki__

**Strong Types, Polish Groups and Topological Dynamics**

__Ayala Rosel__

**Definable One Dimensional Topologies in O-minimal Structures**

Special thanks to Kobi for the local organization!

**17.12.2017 - Ben Gurion University**

**17.12.2017 - Ben Gurion University**

__Daniel Palacin__

**Vapnik-Chervonenkis density, dp-rank and groups.**

In this talk, I will present the definitions of Vapnik-Chernovenkis dimension and density, and explain some links with NIP groups. Furthermore, I will discuss the related notion of dp-rank and analyze these two notions in the context of abelian groups.

__Daoud Siniora__

**Kechris-Rosendal Characterization of Ample Generics**

Special thanks to Omer for the local organizing and the delicious Sufganiyot!

**07.11.2017 - Hebrew University Jerusalem**

**07.11.2017 - Hebrew University Jerusalem**

__Nadav Meir__

In a previous work, we have studied a notion of infinite products induced by trees. This construction, up to elementarily equivalence, generalizes the lexicographic order, taken on for a sequence of partially ordered sets . We have shown that a product of ultrahomogeneous structures is ultrahomogeneous. In this inquiry, we will look into attempts to generalize this further and attempt to represent this construction as an ultraproduct of the finite products which are contained in it. We will further ask how this can be connected to multidimensional asymptotic classes and multidimensional exact classes in the sense of S. Anscombe, H.D. Macpherson, C. Steinhorn and D. Wolf. (and hopefully, no one has been forgotten). Specifically, we hope to answer a question by H.D. Macpherson: "Is there an m.e.c with an ultraproduct with a non-simple theory".

__Itay Kaplan__