10 research outputs found
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
Residue field domination in some henselian valued fields
We generalize previous results about stable domination and residue field
domination to henselian valued fields of equicharacteristic 0 with bounded
Galois group, and we provide an alternate characterization of stable domination
in algebraically closed valued fields for types over parameters in the field
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