DEFINABILITY OF HENSELIAN VALUATIONS BY CONDITIONS ON THE VALUE GROUP
نویسندگان
چکیده
Abstract Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any valuation whose group is not closed in divisible hull definable language of rings, using one parameter. Thereby strengthen known results. Moreover, this case, parameter optimal sense cannot obtain parameters. To end, present construction method for t -Henselian non-Henselian ordered field elementarily equivalent to with specified
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15 صفحه اولRelative decidability and definability in henselian valued fields
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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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2022
ISSN: ['1943-5886', '0022-4812']
DOI: https://doi.org/10.1017/jsl.2022.34