NIP henselian valued fields
نویسندگان
چکیده
منابع مشابه
When Does Nip Transfer from Fields to Henselian Expansions?
Let K be an NIP field and let v be a henselian valuation on K. We ask whether (K, v) is NIP as a valued field. By a result of Shelah, we know that if v is externally definable, then (K, v) is NIP. Using the definability of the canonical p-henselian valuation, we show that whenever the residue field of v is not separably closed, then v is externally definable. We also give a weaker statement for...
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Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: fir...
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We give a de nition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp((t)), which works uniformly for all p and all nite eld extensions of these elds, and in many other Henselian valued elds as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modi cation of the language of Macintyre. Furthermore, we show the negative result th...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2019
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-019-00685-8