Results 1 to 10 of about 21,674,610 (304)
Valuative trees over valued fields [PDF]
Journal of Algebra, 2023 For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrowΛ$ of ordered groups, we analyze the structure of the tree formed by all $Λ$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we find a model for the tree of all equivalence classes of valuations on $K[x]$ (without fixing their value group ...
Alberich Carramiñana, Maria +3 more
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Valued fields, metastable groups [PDF]
Selecta Mathematica, 2019 We introduce a class of theories called metastable, including the theory of algebraically closed valued fields (ACVF) as a motivating example. The key local notion is that of definable types dominated by their stable part. A theory is metastable (over a sort $Γ$) if every type over a sufficiently rich base structure can be viewed as part of a $Γ ...
Hrushovski, Ehud +1 more
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Residue field domination in some henselian valued fields [PDF]
Model Theory, 2023 We generalize previous results about stable domination and residue field domination to henselian valued fields of equicharacteristic 0 with bounded Galois group, and we provide an alternate characterization of stable domination in algebraically closed valued fields for types over parameters in the field sort.
Ealy, Clifton +2 more
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NIP henselian valued fields [PDF]
Archive for Mathematical Logic, 2019 11 ...
Franziska Jahnke, Pierre Simon
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Burden in Henselian valued fields [PDF]
Annals of Pure and Applied Logic, 2023 In the spirit of the Ax-Kochen-Ershov principle, we show that in certain cases the burden of a Henselian valued field can be computed in terms of the burden of its residue field and that of its value group. To do so, we first see that the burden of such a field is equal to the burden of its RV-sort.
Pierre Touchard
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CONTRACTING ENDOMORPHISMS OF VALUED FIELDS
Journal of the Institute of Mathematics of Jussieu, 2023 AbstractWe prove that the class of separably algebraically closed valued fields equipped with a distinguished Frobenius endomorphism $x \mapsto x^q$ is decidable, uniformly in q. The result is a simultaneous generalization of the work of Chatzidakis and Hrushovski (in the case of the trivial valuation) and the work of the first author and Hrushovski (
Yuval Dor, Yatir Halevi
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DP-MINIMAL VALUED FIELDS [PDF]
The Journal of Symbolic Logic, 2017 AbstractWe show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.
Jahnke, Franziska +2 more
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Residue Field Domination in Real Closed Valued Fields [PDF]
Notre Dame Journal of Formal Logic, 2019 22 ...
Ealy, Clifton +2 more
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Computable valued fields [PDF]
Archive for Mathematical Logic, 2017 We investigate the computability-theoretic properties of valued fields, and in particular algebraically closed valued fields and $p$-adically closed valued fields. We give an effectiveness condition, related to Hensel's lemma, on a valued field which is necessary and sufficient to extend the valuation to any algebraic extension. We show that there is a
M. Harrison-Trainor
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On the hyperfields associated to valued fields [PDF]
Journal of Pure and Applied Algebra, 2022 One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field.
Alessandro Linzi, Pierre Touchard
semanticscholar +1 more source