27 research outputs found
On \omega-categorical, generically stable groups
We prove that each \omega-categorical, generically stable group is
solvable-by-finite.Comment: 11 page
Superrosy dependent groups having finitely satisfiable generics
We study a model theoretic context (finite thorn rank, NIP, with finitely
satisfiable generics) which is a common generalization of groups of finite
Morley rank and definably compact groups in o-minimal structures. We show that
assuming thorn rank 1, the group is abelian-by-finite, and assuming thorn rank
2 the group is solvable by finite. Also a field is algebraically closed
On the topological dynamics of automorphism groups; a model-theoretic perspective
We give a model-theoretic treatment of the fundamental results of
Kechris-Pestov-Todor\v{c}evi\'{c} theory in the more general context of
automorphism groups of not necessarily countable structures. One of the main
points is a description of the universal ambit as a certain space of types in
an expanded language. Using this, we recover various results of
Kechris-Pestov-Todor\v{c}evi\'{c}, Moore, Ngyuen Van Th\'{e}, in the context of
automorphism groups of not necessarily countable structures, as well as Zucker