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Remarks around the non-existence of difference-closure

Logic 2023-11-08 v2

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.

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Cite

@article{arxiv.2004.05592,
  title  = {Remarks around the non-existence of difference-closure},
  author = {Zoé Chatzidakis},
  journal= {arXiv preprint arXiv:2004.05592},
  year   = {2023}
}

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R2 v1 2026-06-23T14:48:28.702Z