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Preprint Number 761
761. Arno Fehm
Elementary geometric local-global principles for fields
Submission date: 19 August 2014
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:
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