Simplicity simplified.
Singular properties of Morley rank
Small profinite m-stable groups
A small profinite m-stable group has an open abelian subgroup of finite ℳ-rank and finite exponent.
Some model theory of SL(2,ℝ)
We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on ). We also show that the “Ellis group” (r*I,*) is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.
Stabilité des corps séparablement clos
Strongly determined types and G-compactness
We study connections between G-compactness and existence of strongly determined types.
Suites d'indicernables dans les théories stables
Superstability in simple finitary AECs
We continue the study of finitary abstract elementary classes beyond ℵ₀-stability. We suggest a possible notion of superstability for simple finitary AECs, and derive from this notion several good properties for independence. We also study constructible models and the behaviour of Galois types and weak Lascar strong types in this context. We show that superstability is implied by a-categoricity in a suitable cardinal. As an application we prove the following theorem: Assume that is a simple, tame,...