Submission date: 12 April 2020

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 closure, and this closure is unique up to isomorphism over K.

Mathematics Subject Classification: 03C50, 03C60, 03C98, 12HXX

Keywords and phrases:

Full text arXiv 2004.05592: pdf, ps.