scholarly journals HENSELIAN VALUED FIELDS AND inp-MINIMALITY

2019 ◽  
Vol 84 (4) ◽  
pp. 1510-1526
Author(s):  
ARTEM CHERNIKOV ◽  
PIERRE SIMON
Keyword(s):  
Type Result ◽  
Valued Fields ◽  
Henselian Valued Fields

AbstractWe prove that every ultraproduct of p-adics is inp-minimal (i.e., of burden 1). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic 0 in the RV language.

Model Theory of Henselian Valued Fields

1989 ◽  
pp. v-vi
Author(s):  
H.-D. Ebbinghaus ◽  
J. Fernandez-Prida ◽  
M. Garrido ◽  
D. Lascar ◽  
M. Rodriquez Artalejo
Keyword(s):  
Model Theory ◽  
Valued Fields ◽  
Henselian Valued Fields

On factorization of polynomials in henselian valued fields

2018 ◽  
Vol 46 (7) ◽  
pp. 3205-3221 ◽  
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields ◽  
Factorization Of Polynomials

scholarly journals Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

2013 ◽  
Vol 164 (12) ◽  
pp. 1236-1246 ◽  
Author(s):  
Raf Cluckers ◽  
Jamshid Derakhshan ◽  
Eva Leenknegt ◽  
Angus Macintyre
Keyword(s):  
Valued Fields ◽  
Valuation Rings ◽  
Henselian Valued Fields ◽  
Residue Fields

Onpth Roots in Henselian Valued Fields

2007 ◽  
Vol 35 (2) ◽  
pp. 435-442
Author(s):  
Saurabh Bhatia ◽  
Sudesh K. Khanduja
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields

On finite intersections of ?henselian valued? fields

1985 ◽  
Vol 52 (1-3) ◽  
pp. 37-61 ◽  
Author(s):  
Bernhard Heinemann
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields

scholarly journals ON THE MAIN INVARIANT OF ELEMENTS ALGEBRAIC OVER A HENSELIAN VALUED FIELD

2002 ◽  
Vol 45 (1) ◽  
pp. 219-227 ◽  
Author(s):  
Kamal Aghigh ◽  
Sudesh K. Khanduja
Keyword(s):  
Upper Bound ◽  
Algebraic Closure ◽  
Subject Classification ◽  
Unique Extension ◽  
Valued Fields ◽  
Valued Field ◽  
Henselian Valued Fields ◽  
Alpha Beta ◽  
Henselian Valuation

AbstractLet $v$ be a henselian valuation of a field $K$ with value group $G$, let $\bar{v}$ be the (unique) extension of $v$ to a fixed algebraic closure $\bar{K}$ of $K$ and let $(\tilde{K},\tilde{v})$ be a completion of $(K,v)$. For $\alpha\in\bar{K}\setminus K$, let $M(\alpha,K)$ denote the set $\{\bar{v}(\alpha-\beta):\beta\in\bar{K},\ [K(\beta):K] \lt [K(\alpha):K]\}$. It is known that $M(\alpha,K)$ has an upper bound in $\bar{G}$ if and only if $[K(\alpha):K]=[\tilde{K}(\alpha):\tilde{K}]$, and that the supremum of $M(\alpha,K)$, which is denoted by $\delta_{K}(\alpha)$ (usually referred to as the main invariant of $\alpha$), satisfies a principle similar to the Krasner principle. Moreover, each complete discrete rank 1 valued field $(K,v)$ has the property that $\delta_{K}(\alpha)\in M(\alpha,K)$ for every $\alpha\in\bar{K}\setminus K$. In this paper the authors give a characterization of all those henselian valued fields $(K,v)$ which have the property mentioned above.AMS 2000 Mathematics subject classification: Primary 12J10; 12J25; 13A18

A study of irreducible polynomials over henselian valued fields via distinguished pairs

2014 ◽  
pp. 1-10
Author(s):  
Kamal Aghigh ◽  
Anuj Bishnoi ◽  
Sudesh Khanduja ◽  
Sanjeev Kumar
Keyword(s):  
Irreducible Polynomials ◽  
Valued Fields ◽  
Henselian Valued Fields

scholarly journals DEFINABLE HENSELIAN VALUATIONS

2015 ◽  
Vol 80 (1) ◽  
pp. 85-99 ◽  
Author(s):  
FRANZISKA JAHNKE ◽  
JOCHEN KOENIGSMANN
Keyword(s):  
Galois Group ◽  
Residue Field ◽  
Absolute Galois Group ◽  
Valued Fields ◽  
Valued Field ◽  
Henselian Valued Fields ◽  
The Absolute ◽  
Henselian Valuation

AbstractIn this note we investigate the question when a henselian valued field carries a nontrivial ∅-definable henselian valuation (in the language of rings). This is clearly not possible when the field is either separably or real closed, and, by the work of Prestel and Ziegler, there are further examples of henselian valued fields which do not admit a ∅-definable nontrivial henselian valuation. We give conditions on the residue field which ensure the existence of a parameter-free definition. In particular, we show that a henselian valued field admits a nontrivial henselian ∅-definable valuation when the residue field is separably closed or sufficiently nonhenselian, or when the absolute Galois group of the (residue) field is nonuniversal.

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