Definable groups in topological differential fields

Abstract

For certain theories of existentially closed topological differential fields, we show that there is a strong relationship between L ∪ {D}-definable sets and their Lreducts, where L is a relational expansion of the field language and D a symbol for a derivation. This enables us to associate with an L ∪ {D}-definable group in models of such theories, a local L-definable group. As a byproduct, we show that in closed ordered differential fields, one has the descending chain condition on centralisers.