Journal of Symbolic Logic

Quantifier Elimination in Tame Infinite p-Adic Fields

Ingo Brigandt

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We give an answer to the question as to whether quantifier elimination is possible in some infinite algebraic extensions of $\mathbb{Q}_p$ ('infinite p-adic fields') using a natural language extension. The present paper deals with those infinite p-adic fields which admit only tamely ramified algebraic extensions (so- called tame fields). In the case of tame fields whose residue fields satisfy Kaplansky's condition of having no extension of p-divisible degree quantifier elimination is possible when the language of valued fields is extended by the power predicates P$_n$, introduced by Macintyre and, for the residue field, further predicates and constants. For tame infinite p-adic fields with algebraically closed residue fields an extension by P$_n$ predicates is sufficient.

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J. Symbolic Logic, Volume 66, Issue 3 (2001), 1493-1503.

First available in Project Euclid: 6 July 2007

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Brigandt, Ingo. Quantifier Elimination in Tame Infinite p-Adic Fields. J. Symbolic Logic 66 (2001), no. 3, 1493--1503.

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