The model theory of separably tame valued fields
نویسندگان
چکیده
منابع مشابه
The 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 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 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 ...
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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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These notes focus mainly on the model theory of algebraically closed valued fields (loosely referred to as ACVF). This subject begins with work by A. Robinson in the 1950s (see the proof of model completeness of algebraically closed valued fields in [41]). Thus, it predates the major work of Ax-Kochen and Ershov around 1963; and, unlike the latter (and much subsequent work on quantifier elimina...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.09.022