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Recovering the cluster picture of a polynomial over a discretely valued field [PDF]
Royal Society Open ScienceFor [Formula: see text], a separable polynomial of degree [Formula: see text] over a discretely valued field [Formula: see text], we describe how the cluster picture of [Formula: see text] over [Formula: see text], in other words, the set of tuples ...
Lilybelle Cowland Kellock
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Valuations on Structures More General Than Fields
Computer Sciences & Mathematics Forum, 2023 Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some ...
Alessandro Linzi
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Interpretable fields in various valued fields
Advances in Mathematics, 2022 Let $\mathcal{K}=(K,v,\ldots)$ be a dp-minimal expansion of a non-trivially valued field of characteristic $0$ and $\mathcal{F}$ an infinite field interpretable in $\mathcal{K}$. Assume that $\mathcal{K}$ is one of the following: (i) $V$-minimal, (ii) power bounded $T$-convex, or (iii) $P$-minimal (assuming additionally in (iii) generic ...
Halevi, Yatir +2 more
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α-Generalized Semantic Resolution Method in Linguistic Truth-valued Propositional Logic P(X) [PDF]
International Journal of Computational Intelligence Systems, 2014 This paper is focused on α-generalized semantic resolution automated reasoning method in linguistic truth-valued lattice-valued propositional logic.
Jiafeng Zhang, Yang Xu, Xingxing He
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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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α-Resolution Method for Lattice-valued Horn Generalized Clauses in Lattice-valued Propositional Logic Systems [PDF]
International Journal of Computational Intelligence Systems, 2015 In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic system ℒ P(X) based on lattice implication algebra.
Weitao Xu +4 more
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NIP henselian valued fields [PDF]
Archive for Mathematical Logic, 2019 11 ...
Franziska Jahnke, Pierre Simon
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Valuative trees over valued fields
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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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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Single-Valued Neutro Hyper BCK-Subalgebras
Journal of Mathematics, 2021 The purpose of this paper is to introduce the notation of single-valued neutrosophic hyper BCK-subalgebras and a novel concept of neutro hyper BCK-algebras as a generalization and alternative of hyper BCK-algebras, that have a larger applicable field. In
M. Hamidi, F. Smarandache
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