Quantifier elimination and minimality conditions in algebraically closed valued fields

2010/06/07 by Yimu Yin, Yin, Yimu · 5 citations
Mathematics · Computer Science · #Advanced Topology and Set Theory #semigroups and automata theory #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.1006.1393

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.

Cited by

• Bounded integral and motivic Milnor fiber
• Additive invariants in o-minimal valued fields
• Special transformations in algebraically closed valued fields
• Non-archimedean stratifications in power bounded T-convex fields
• Integration in algebraically closed valued fields with sections

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