Quantifier elimination and minimality conditions in algebraically closed valued fields

Yimu Yin

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arXiv · 1006.1393

Quantifier elimination and minimality conditions in algebraically closed valued fields

Yimu Yin

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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.

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BibTeX RIS

Yimu Yin. 2010-06-07. Quantifier elimination and minimality conditions in algebraically closed valued fields. https://arxiv.org/abs/1006.1393

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