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Preprint Number 699

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699. Ehud Hrushovski
Imaginaries and definable types in algebraically closed valued fields

Submission date: 28 March 2014.


The text is based on notes from a class entitled Model Theory of Berkovich Spaces, given at the Hebrew University in the fall term of 2009, and retains the flavor of class notes. It includes an exposition of material from [HMM-1], [HMM-2] and [HL], regarding definable types in the model completion of the theory of valued fields, and the classification of imaginary sorts. The latter is given a new proof, based on definable types rather than invariant types, and on the notion of generic reparametrization. I also try to bring out the relation to the geometry of [HL] - stably dominated definable types as the model theoretic incarnation of a Berkovich point.

[HMM-1] D. Haskell, E. Hrushovski, D. Macpherson, Definable sets in algebraically closed valued fields: elimination of imaginaries, J. Reine Angew. Math. 597 (2006), 175 - 236.
[HMM-2] D. Haskell, E. Hrushovski, D. Macpherson, Stable domination and independence in algebraically closed valued fields, Lecture Notes in Logic, 30. Association for Symbolic Logic, Chicago, IL; Cambridge University Press, Cambridge, 2008.
[HL] E. Hrushovski, F. Loeser, Non-Archimedean tame topology and stably dominated types, arXiv:1009.0252.

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Full text arXiv 1403.7326: pdf, ps.

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