Keisler measures were introduced in the late 80's by Keisler but they became central objects in model theory only recently with the development of NIP theories. This led naturally to the question of whether there might be a parallel theory of measures in other tame classes, especially in the simple theories where pseudofinite counting measures supply natural and interesting examples. We will describe some first steps toward establishing such a theory, based on Keisler randomizations and the theory of independence for NSOP1 theories in continuous logic.

We shall try to prove some surprising (and hopefully, correct) theorems about the relationship between the club principle (Hebrew: tiltan) and the splitting number, with respect to the classical s at omega and the generalized s at supercompact cardinals.

We shall prove that there is a sequence of Boolean algebras for which the ultraproduct of the lengths divided by an ultrafilter is strictly less than the length of the product algebra. This is a joint work with Saharon Shelah.

Better lucky than smart: realizing a quasi-generic class of measure preserving transformations as diffeomorphisms. Speaker: Matthew Foreman Abstract: In 1932, von Neumann proposed classifying measure preserving diffeomorphisms up to measure isomorphism. Joint work with B. Weiss shows this is impossible in the sense that the corresponding equivalence relation is not Borel; hence impossible to capture using countable methods.

Speaker: Elad Levi Algebraic regularity lemma for hypergraphs Abstract: Szemer´edi’s Regularity Lemma is a fundamental tool in graph theory. It states that for every large enough graph, the set of vertices has a partition A1,..,Ak, such that for almost every two subsets Ai,Aj the induced bipartite graph on (Ai,Aj) is regular, i.e. similar to a random bipartite graph up to a given error.

In [Sh771] Shelah rediscovered an old result of Dudley on the non-admissibility of a Polish group topology on an uncountable free group. Crucial to his proof is a so-called Compactness Lemma for Polish groups, concerning satisfaction of algebraic equations for certain sequences of group elements converging to 0 (in distance).

The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.

This talk will be largely based on a paper by Joseph Shipman with the same title. We will discuss some variations of Fubini type theorems. The focus will be on what is known as "strong Fubini type theorems". Apparently these versions were proved to be independent of ZFC,and our main aim will be to sketch a proof of this result. We will assume basic knowledge in measure theory. Aside from that, the material is rather self contained.

Weak Prediction Principles Speaker: Yair Hayut Abstract: Jensen's diamond is a well studied prediction principle. It holds in L (and other core models), and in many cases it follows from local instances of GCH. In the talk I will address a weakening of diamond (due to Shaleh and Abraham) and present Abraham's theorem about the equivalence between weak diamond and a weak consequence of GCH. Abraham's argument works for successor cardinals. I will discuss what is known and what is open for inaccessible cardinals. This is a joint work with Shimon Garti and Omer Ben-Neria.

Abstract: The set theoretic generalizations of algebras have been introduced in the 1960s to give a set theoretic interpretation of usual algebraic structures. The shift in perspective from algebra to set theory is that in set theory the focus is on the collection of possible algebras and sub-algebras on specific cardinals rather than on particular algebraic structures. The study of collections of algebras and sub-algebras has generated many well-known problems in combinatorial set theory (e.g., Chang’s conjecture and the existence of small singular Jonsson cardinals).

Arbault sets (briefly, A-sets) were first introduced by Jean Arbault in the context of Fourier analysis. One of his major results concerning these sets,asserts that the union of an A-set with a countable set is again an A-set. The next obvious step is to ask what happens if we replace the word "countable" by א_1. Apparently, an א_1 version of Arbault's theorem is independent of ZFC. The aim of this talk would be to give a proof (as detailed as possible) of this independence result. The main ingredients of the proof are infinite combinatorics and some very basic Fourier analysis.

This talk is about three published papers of mine that form my phd. In the first two chapters I focus in the model theory of real closed fields and in the third one I take one step back and investigate in greater genearility dependent theories. The results are the following: 1. Boundedness criterion for rational functions over generalized semi-algebraic sets in real closed fields. 2. Positivity criterion for polynomials over generalized semi-algebraic sets in real closed valued fields.

The notion of reflection plays a central role in modern Set Theory since the descovering of the well-known Lévy and Montague \textit{Reflection principle}. For any $n\in\omega$, let $C^{(n)}$ denote the class of all ordinals $\kappa$ which correctly interprets the $\Sigma_n$-statements of the universe, with parametes in $V_\kappa$.

Non-equational stable groups. Speaker: Rizos Sklinos Abstract: The notion of equationality has been introduced by Srour and further developed by Pillay-Srour. It is best understood intuitively as a notion of Noetherianity on instances of first-order formulas. A first-order theory is equational when every first-order formula is equivalent to a boolean combination of equations. Equationality implies stability and for many years these two notions were identified, as only an "artificial" example of Hrushovski (a tweaked pseudo-space) was witnessing otherwise. Recently Sela proved that the