scholarly journals Some model theory for Henselian valued fields

1978 ◽  
Vol 55 (2) ◽  
pp. 191-212 ◽  
Author(s):  
Serban A Basarab
Author(s):  
H.-D. Ebbinghaus ◽  
J. Fernandez-Prida ◽  
M. Garrido ◽  
D. Lascar ◽  
M. Rodriquez Artalejo

Author(s):  
Matthias Aschenbrenner ◽  
Lou van den Dries ◽  
Joris van der Hoeven

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.


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

2019 ◽  
Vol 84 (4) ◽  
pp. 1510-1526
Author(s):  
ARTEM CHERNIKOV ◽  
PIERRE SIMON

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.


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

2018 ◽  
Vol 46 (7) ◽  
pp. 3205-3221 ◽  
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan

2013 ◽  
Vol 164 (12) ◽  
pp. 1236-1246 ◽  
Author(s):  
Raf Cluckers ◽  
Jamshid Derakhshan ◽  
Eva Leenknegt ◽  
Angus Macintyre

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