Definable groups in topological fields with a generic derivation
Françoise Point (Université de Mons-Hainaut)
Abstract: We study a class of tame -theories of topological fields and their extensions by a generic derivation . The topological fields under consideration include henselian valued fields of characteristic 0 and real closed fields. We axiomatize the class of the existentially closed -expansions. We show that has -open core (i.e., every -definable open set is -definable) and derive both a cell decomposition theorem and a transfer result of elimination of imaginaries. Other tame properties of such as relative elimination of field sort quantifiers, NIP and distality also transfer to . \par Then letting be a model of and a -saturated elementary extension of , we first associate with an -definable group in , a pro--definable set in which the differential prolongations of elements of are dense, using the -open core property of . Following the same ideas as in the group configuration theorem in o-minimal structures as developed by K. Peterzil, we construct a type -definable topological group , acting on a -infinitesimal neighbourhood of a generic element of in a faithful, continuous and transitive way. Further is dense in and the action of coincides with the one induced by the initial -group action. \par The first part of this work is joint with Pablo Cubid\`es Kovacsics.
logicnumber theory
Audience: researchers in the topic
Series comments: Description: Seminar on all areas of logic
Organizer: | Wesley Calvert* |
*contact for this listing |