Mathematical Logic Quarterly 53 (3):237-246 (2007)

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
Keywords analytic structures  Quantifier elimination  valued fields
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DOI 10.1002/malq.200610042
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On Some Definable Sets Over Fields with Analytic Structure.Y. Fırat Çelı̇kler - 2010 - Annals of Pure and Applied Logic 161 (4):599-616.

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