Topological fields with a generic derivation

被引:2
作者
Kovacsics, Pablo Cubides [1 ]
Point, Francoise [2 ,3 ]
机构
[1] Univ Los Andes, Dept Matemat, Carrera 1 18A-12,Edificio H, Bogota 111711, Colombia
[2] UMons, Dept Math De Vinci, 20 Pl Parc, B-7000 Mons, Belgium
[3] Fonds Natl Rech Sci FNRS FRS, Brussels, Belgium
基金
欧洲研究理事会;
关键词
Topological fields; Differential fields; Generic derivations; Elimination of imaginaries; Open core; DIFFERENTIAL FIELDS; DEFINABLE SETS; DISTAL; DIMENSION;
D O I
10.1016/j.apal.2022.103211
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a class of tame G-theories T of topological fields and their G & delta;-extension T & delta;* by a generic derivation & delta;. The topological fields under consideration include henselian valued fields of characteristic 0 and real closed fields. We show that the associated expansion by a generic derivation has G-open core (i.e., every G & delta;-definable open set is G-definable) and derive both a cell decomposition theorem and a transfer result of elimination of imaginaries. Other tame properties of T such as relative elimination of field sort quantifiers, NIP and distality also transfer to T & delta;*. As an application, we derive consequences for the corresponding theories of dense pairs. In particular, we show that the theory of pairs of real closed fields (resp. of p-adically closed fields and real closed valued fields) admits a distal expansion. This gives a partial answer to a question of P. Simon.& COPY; 2023 Elsevier B.V. All rights reserved.
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页数:38
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