scholarly journals Some model theory for Henselian valued fields

1978 ◽  
Vol 55 (2) ◽  
pp. 191-212 ◽  
Author(s):  
Serban A Basarab
Keyword(s):  
Model Theory ◽  
Valued Fields ◽  
Henselian Valued Fields

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

Valued Fields

2017 ◽  
Author(s):  
Matthias Aschenbrenner ◽  
Lou van den Dries ◽  
Joris van der Hoeven
Keyword(s):  
Field Theory ◽  
Model Theory ◽  
Newton Diagram ◽  
Basic Field ◽  
Valued Fields ◽  
Basic Properties ◽  
Basic Model ◽  
Valued Field ◽  
Henselian Valued Fields ◽  
Basic Facts

This chapter introduces the reader to basic field theory by focusing on valued fields. It first considers valuations on fields before discussing the basic properties of valued fields, with emphasis on extensions. It then describes pseudoconvergence in valued fields, along with henselian valued fields. It also shows how to decompose a valuation on a field into simpler ones, leading to an analysis of various special types of pseudocauchy sequences. Because the valuation of is compatible with its natural ordering, some basic facts about fields with compatible ordering and valuation are presented. The chapter concludes by reviewing some basic model theory of valued fields as well as the Newton diagram and Newton tree of a polynomial over a valued field.

scholarly journals The model theory of separably tame valued fields

2016 ◽  
Vol 447 ◽  
pp. 74-108 ◽  
Author(s):  
Franz-Viktor Kuhlmann ◽  
Koushik Pal
Keyword(s):  
Model Theory ◽  
Valued Fields

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 valued fields

2018 ◽  
pp. 151-180
Author(s):  
Martin Hils
Keyword(s):  
Model Theory ◽  
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
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