Submission date: 13 March 2009.

Abstract:

We give a presentation of the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan. We limit our attention to a simple major subclass of V-minimal theories of the form ACVF^0_S, that is, the theory of algebraically closed valued fields of pure characteristic 0 expanded by a (VF, Gamma)-generated substructure S in the language L_RV. The main advantage of this subclass is the presence of syntax. It enables us to simplify the arguments with many new technical details while following the major steps of the Hrushovski-Kazhdan theory.

Mathematics Subject Classification: 03C60, 11S80

Keywords and phrases:

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