Remarks around the non-existence of difference-closure

Zoé Chatzidakis (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

This paper shows that in general, difference fields do not have a difference closure. However, we introduce a stronger notion of closure (κ-closure), and show that every alge- braically closed difference field K of characteristic 0, with fixed field satisfying a certain natural condition, has a κ-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. 2023. ⟨hal-02612599v4⟩