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Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)$
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Ehud Hrushovski and François Loeser

Print publication date: 2016

Print ISBN-13: 9780691161686

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161686.001.0001

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Preliminaries

Preliminaries

Chapter:
(p.8) Chapter Two Preliminaries
Source:
Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)
Author(s):

Ehud Hrushovski

François Loeser

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691161686.003.0002

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

Keywords:   definable set, definable type, orthogonality, stable domination, algebraically closed valued field, ind-definable set, stably dominated type, stably dominated, pseudo-Galois covering, substructure

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