Imaginaries, invariant types and pseudo p-adically closed fields

In this paper, we give a general criterion for elimination of imaginaries using an abstract independence relation. We also study germs of definable functions at certain well-behaved invariant types. Finally we apply these results to prove the elimination of imaginaries in bounded pseudop-adically closed fields.ValCoMo/[ANR-13-BS01-0006]//UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA

Groups with f-generics in NTP2 and PRC fields

We study groups with f-generic types definable in bounded PRC fields. Along the way, we generalize part of the basic theory of definably amenable NIP groups to NTP2theories and prove variations on Hrushovski’s stabilizer theorem.ValCoMo /[ANR-13-BS01-0006]//UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA

Groups definable in partial differential fields with an automorphism

In this paper we study groups definable in existentially closed partial differential fields of characteristic 0 with an automorphism which commutes with the derivations. In particular, we study Zariski dense definable subgroups of simple algebraic groups, and show an analogue of Phyllis Cassidy’s result for partial differential fields. We also show that these groups have a smallest definable subgroup of finite index.Universidad de Costa Rica/[821-C0-464]/UCR/Costa RicaUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA