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- Title
Preliminaries.
- Authors
Hrushovski, Ehud; Loeser, François
- Abstract
In 2.1-2.6 we recall some model theoretic notions we shall use in an essential way in this work: definable, pro-definable and ind-definable sets, definable types, orthogonality to a definable set, stable domination. In 2.7-2.9 we consider more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and recall in particular some results of [19] and [20] we rely on. In 2.10 we describe the definable types concentrating on a stable definable V as an ind-definable set. In 2.11, we prove a key result allowing us to view definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, in 2.12 we discuss the notion of pseudo-Galois coverings that we shall use in Chapter 6. We will rapidly recall the basic model theoretic notions of which we make use, but we recommend to the non-model theoretic reader an introduction such as [34] (readers seeking a more comprehensive text on stability may also consult [33]).
- Subjects
DEFINABILITY theory (Mathematical logic); ORTHOGONAL functions; BOOLEAN algebra; ISOMORPHISM (Mathematics); SET theoretic topology
- Publication
Princeton Annals of Mathematics Studies, 2016, Issue 192, p8
- ISSN
0066-2313
- Publication type
Article