Submission date: 19 August 2014

Abstract:

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

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.

Mathematics Subject Classification: 12E30, 12L12, 14G05, 12J12

Keywords and phrases:

Full text arXiv 1408.4231: pdf, ps.