Quantifier elimination and minimality conditions in algebraically closed valued fields

Abstract

A Basarab-Kuhlmann style language L_RV is introduced in the Hrushovski-Kazhdan integration theory. The theory ACVF of algebraically closed valued fields formulated in this language admits quantifier elimination. In this paper, using well-known facts in the theory of valued fields, we give a straightforward proof of this fact. We also show that two expansions of ACVF, one with a section of the entire RV-sort and the other with a section of the residue field, admit quantifier elimination. Thereafter we show that, in terms of certain minimality conditions, the three theories are distinct geometrically.

submitted

References in corpus (3)

• Motivic Poisson summation
• Integration in algebraically closed valued fields
• Fourier transform of the additive group in algebraically closed valued fields

Cited by in corpus (7)

• Fourier transform of the additive group in algebraically closed valued fields
• Additive invariants in o-minimal valued fields
• Special transformations in algebraically closed valued fields
• Generalized Euler characteristic in power-bounded T-convex valued fields
• Integration in algebraically closed valued fields with sections
• Bounded integral and motivic Milnor fiber
• Non-archimedean stratifications in power bounded $T$-convex fields