Learn More
The questions this manuscript addresses arose in the course of an investigation of the imaginary sorts in ultraproducts of p-adic fields. These were shown to be understandable given the imaginary sorts of certain finite-dimensional vector spaces over the residue field. The residue field is pseudo-finite, and the imaginary elements there were previously(More)
We study forking, Lascar strong types, Keisler measures and defin-able groups, under an assumption of N IP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if p = tp(b/A) does not fork over A then the Lascar strong type of b over A coincides with the compact strong type of b over A and any global nonforking(More)
This paper contains a series of easy constructions and observations relating to the Lascar group and to simple theories. 1 In x1 we review basic model theoretic ideas, relating mostly to model completion and saturated models. We do so in order to introduce a framework very slightly more general than the usual rst-order one that will be useful to us, and(More)
It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K n of certain definable R-submodules of K n (for all n ≥ 1). The proof involves the development of a theory of independence for unary types, which play the role of 1-types,(More)
This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in(More)