This book addresses a gap in the model-theoretic understanding of
valued fields that had 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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