We discuss measures, invariant measures on definable groups, and genericity, often in an
NIP (failure of the independence property) environment. We complete the proof of the third …

We study forking, Lascar strong types, Keisler measures and definable groups, under an
assumption of NIP (not the independence property), continuing aspects of the paper [16] …

We study type-definable subgroups of small index in definable groups, and the structure on
the quotient, in first order structures. We raise some conjectures in the case where the …

TOPOLOGICAL DYNAMICS OF DEFINABLE GROUP ACTIONS Introduction. Assume G is a
group. By a G-flow we mean a compact topological spa Page 1 THE JOURNAL OF SYMBOLIC …

We introduce a class of theories called metastable, including the theory of algebraically
closed valued fields (ACVF ACVF) as a motivating example. The key local notion is that of …

We give examples of definable groups G (in a saturated model, sometimes o-minimal) such
that G00≠ G000, yielding also new examples of “non G-compact” theories. We also prove …

Kirszbraun's theorem states that every Lipschitz map S→ ℝ n, where S⊆ ℝ m, has an
extension to a Lipschitz map ℝ m→ ℝ n with the same Lipschitz constant. Its proof relies on …

We formulate p-adic analogues of the o-minimal group conjectures from the works of
Hrushovski, Peterzil and Pillay [J. Amer. Math. Soc., to appear] and Pillay [J. Math. Log. 4 …

We prove several structural results on definable, definably compact groups G in o-minimal
expansions of real closed fields such as (i) G is definably an almost direct product of a …

Let M=< M,+,<, 0,{λ} λЄD> be an ordered vector space over an ordered division ring D, and
G=< G,⊕, eG> an n-dimensional group definable in M. We show that if G is definably …