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 many ways like the space of types in a
stable theory. This part begins with an introduction to the key
ideas of stability theory for stably dominated types. Part II
continues with an outline of some classical results in the model
theory of valued fields and explores the application of stable
domination to algebraically closed valued fields. The research
presented here is made accessible to the general model theorist by
the inclusion of the introductory sections of each part.
General
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