We study amenability of definable groups and topological groups, and prove various results,
briefly described below. Among our main technical tools, of interest in its own right, is an …

We study the problem of when, given a homogeneous structure $ M $ and a space $ S $ of
expansions of $ M $, every $\mathrm {Aut}(M) $-invariant probability measure on $ S $ is …

We initiate the study of p-adic algebraic groups G from the stability-theoretic and definable
topological-dynamical points of view, that is, we consider invariants of the action of G on its …

We introduce the notion of first order amenability, as a property of a first order theory $ T $:
every complete type over $\emptyset $, in possibly infinitely many variables, extends to an …

Let ℭ be a monster model of an arbitrary theory T, let α ̄ be any (possibly infinite) tuple of
bounded length of elements of ℭ, and let c ̄ be an enumeration of all elements of ℭ (so a …

In the 1970s, structural Ramsey theory emerged as a new branch of combinatorics. This
development came with the isolation of the concepts of the $\mathbf {A} $-Ramsey property …

We introduce and study the model-theoretic notions of absolute connectedness and type-
absolute connectedness for groups. We prove that groups of rational points of split …

We develop some model theory of multi-linear forms, generalizing Granger in the bi-linear
case. In particular, after proving a quantifier elimination result, we show that for an NIP field …

We prove Bogolyubov–Ruzsa-type results for finite subsets of groups with small tripling,|
A3|≤ O (| A|), or small alternation,| AA− 1A|≤ O (| A|). As applications, we obtain a …

We introduce and study model-theoretic connected components of rings as an analogue of
model-theoretic connected components of definable groups. We develop their basic theory …