Quantifier elimination in tame infinite p-adic fields

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  • We give an answer to the question as to whether quantifier elimination is possible in some infinite algebraic extensions of QpQp ('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 Pnn, 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 Pnn predicates is sufficient.

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    Article (Published)
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    © 2001 Association for Symbolic Logic. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
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    • Brigandt, I. (2001). Quantifier elimination in tame infinite p-adic fields. Journal of Symbolic Logic, 66(3), 1493-1503.
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