We work in a first-order setting where structures are spread out over a metric space, with
quantification allowed only over bounded subsets. Assuming a doubling property for the …

We identify a canonical structure J associated to any first-order theory, the {\it space of
definability patterns}. It generalizes the imaginary algebraic closure in a stable theory, and …

We solve two problems from a work of Haskel and Pillay concerning maximal stable
quotients of groups∧-definable in NIP theories. The first result says that if G is a∧-definable …

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 $ G $ be a group with a metric $\mathrm {d} $ invariant under left and right translations,
and let $\bar {\mathbb {D}} _r $ be the ball of radius $ r $ around the identity. A $(k, r) …

We study canonical quotients in model theory, mainly stable quotients of type-definable
groups and invariant types in NIP theories. We extend the modelling property to continuous …

We prove a structure theorem for stable functions on amenable groups, which extends the
arithmetic regularity lemma for stable subsets of finite groups. Given a group $ G $, a …

Let AA be a countable ℵ0‐homogeneous structure. The primary motivation of this work is to
study different amenability properties of (subgroups of) the automorphism group Aut (A) …

We give a proof of the existence of generalized definable locally compact models for
arbitrary approximate subgroups via an application of topological dynamics in model theory …

We study maximal WAP and tame (in the sense of topological dynamics) quotients of $ S_X
(\mathfrak {C}) $, where $\mathfrak {C} $ is a sufficiently saturated (called monster) model of …