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arXiv · 1408.4231

Elementary geometric local-global principles for fields

Arno Fehm
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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.

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Arno Fehm. 2014-08-19. Elementary geometric local-global principles for fields. https://arxiv.org/abs/1408.4231

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