English

Elementary geometric local-global principles for fields

Logic 2014-08-20 v1 Algebraic Geometry

Abstract

We define and investigate a family of local-global principles for fields involving both orderings and p-valuations. This family contains the PAC, PRC and PpC fields and exhausts the class of pseudo classically closed fields. We show that the fields satisfying such a local-global principle form an elementary class, admit diophantine definitions of holomorphy domains, and their orderings satisfy the strong approximation property.

Keywords

Cite

@article{arxiv.1408.4231,
  title  = {Elementary geometric local-global principles for fields},
  author = {Arno Fehm},
  journal= {arXiv preprint arXiv:1408.4231},
  year   = {2014}
}

Comments

final version published in Annals of Pure and Applied Logic, Volume 164, Issue 10, October 2013, Pages 989-1008

R2 v1 2026-06-22T05:33:00.904Z