Definable groups in topological differential fields (1707.07881v1)

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