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SEPARABLY CLOSED VALUED FIELDS: QUANTIFIER ELIMINATION

Published online by Cambridge University Press:  12 August 2016

JIZHAN HONG
JIZHAN HONG*
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES HUAQIAO UNIVERSITY 269 CHENGHUA RD. NORTH QUANZHOU FUJIAN 362021, CHINAE-mail: shuxuef@hqu.edu.cn
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Abstract

It is proved in this article that the theory of separably closed nontrivially valued fields of characteristic p > 0 and imperfection degree e > 0 (e ≤ ∞) has quantifier elimination in the language ${{\cal L}_{p,{\rm{div}}}} = \{ + , - , \times ,0,1\} \cup {\{ {\lambda _{n,j}}(x;{y_1}, \ldots ,{y_n})\} _{0 \le n < \omega ,0 \le j < {p^n}}} \cup \{ |\}$; in particular, when e is finite, the corresponding theory has quantifier elimination in the language ${\cal L} = \{ + , - , \times ,0,1\} \cup \{ {b_1}, \ldots ,{b_e}\} \cup {\{ {\lambda _{e,j}}(x;{b_1}, \ldots ,{b_e})\} _{0 \le j < {p^e}}} \cup \{ |\}$.

Keywords

separably closed valued fieldsquantifier eliminationinfinite imperfection degree
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 887 - 900
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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