Abstract

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 $\kappa$-closure, and this closure is unique up to isomorphism over $K$.

Keywords

Mathematical Subject Classification

Milestones

Authors