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 give examples of (i) a simple theory with a formula (with parameters) which does not fork
over∅ but has μ-measure 0 for every automorphism invariant Keisler measure μ and (ii) a …

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 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 discuss the externally definable Ramsey property, a weakening of the Ramsey property
for relational structures, where the only colourings considered are those that are externally …

How do we randomly sample an infinite sequence from a first order structure? What
properties might hold on almost all random sequences? Which kinds of probabilistic …

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 investigate interactions between Ramsey theory, topological dynamics, and model
theory. We introduce various Ramsey-like properties for first order theories and characterize …

arXiv:2307.11037v1 [math.LO] 20 Jul 2023 Page 1 Forking and invariant measures in NIP
theories Anand Pillay, ∗ Atticus Stonestrom Department of Mathematics, University of Notre …

For a NIP theory T, a sufficiently saturated model equivalence relation on the set of
realizations of p which has stable quotient. This is a counterpart for equivalence relations of …