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Quantifier elimination for the theory of algebraically closed valued fields with analytic structure
Author(s) -
Çelikler Yalın F.
Publication year - 2007
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200610042
Subject(s) - quantifier elimination , parameterized complexity , mathematics , algebraically closed field , normalization (sociology) , algebraic number , algebra over a field , pure mathematics , discrete mathematics , quantifier (linguistics) , calculus (dental) , combinatorics , mathematical analysis , computer science , artificial intelligence , medicine , dentistry , sociology , anthropology
The theory of algebraically closed non‐Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz, and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper. This theorem also has other consequences in the geometry of definable sets. The method of proving quantifier elimination in this paper for an analytic language does not require the algebraic quantifier elimination theorem of Weispfenning, unlike the customary method of proof used in similar earlier analytic quantifier elimination theorems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)