Elementary geometric local–global principles for fields

Annals of Pure and Applied Logic 164 (10):989-1008 (2013)
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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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Denseness results in the theory of algebraic fields.Sylvy Anscombe, Philip Dittmann & Arno Fehm - 2021 - Annals of Pure and Applied Logic 172 (8):102973.

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