Remarks around the non-existence of difference-closure

Zoé Chatzidakis (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

This paper shows that in general, difference fields do not have a difference closure. However, we introduce a stronger notion of closure (kappa-closure), and show that every algebraically closed difference field K of characteristic 0, with fixed field satisfying a certain natural condition, has a closure, and this closure is unique up to isomorphism over K.

Domaines: Logique [math.LO]

Zoé Chatzidakis. Remarks around the non-existence of difference-closure. 2021. ⟨hal-03227381⟩