The algebra and model theory of tame valued fields
نویسندگان
چکیده
منابع مشابه
The Algebra and Model Theory of Tame Valued Fields
A henselian valued field K is called a tame field if its algebraic closure K̃ is a tame extension, that is, the ramification field of the normal extension K̃|K is algebraically closed. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We develop the algebraic theory of tame fields and then prove Ax–Kochen– Ershov Principles for tame fields. This leads to model compl...
متن کاملThe Model Theory of Separably Tame Valued Fields
A henselian valued field K is called separably tame if its separable-algebraic closure K is a tame extension, that is, the ramification field of the normal extension K|K is separable-algebraically closed. Every separable-algebraically maximal Kaplansky field is a separably tame field, but not conversely. In this paper, we prove Ax– Kochen–Ershov Principles for separably tame fields. This leads ...
متن کاملThe model theory of tame valued fields Preliminary version
A henselian valued field K is called a tame field if its separable-algebraic closure Ksep is a tame extension, that is, Ksep is equal to the ramification field of the normal extension Ksep|K. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We prove Ax–Kochen–Ershov Principles for tame fields. This leads to model completeness and completeness results relative to ...
متن کاملNotes on extremal and Tame Valued Fields
We extend the characterization of extremal valued fields given in [1] to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that are extremal. The key to the proof is a model theoretic result about tame valued fields in mixed characteristic. Further, we prove that in an extremal valued field o...
متن کاملModel Theory of Valued Fields
We give a proposal for future development of the model theory of valued fields. We also summarize recent results on p-adic numbers. Let K be a valued field with a valuation map v : K → G ∪ {∞} to an ordered group 1 G; this is a map satisfying (i) v(x) = ∞ if and only if x = 0; (ii) v(xy) = v(x) + v(y) for all x, y ∈ K; (iii) v(x + y) ≥ min{v(x), v(y)} for all x, y ∈ K. We write R for the valuat...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2016
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2014-0029