Elementary geometric local-global principles for fields

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Annals of Pure and Applied Logic. 2013, 164(10), pp. 989-1008. ISSN 0168-0072. eISSN 0168-0072. Available under: doi: 10.1016/j.apal.2013.05.003
Zusammenfassung

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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Fachgebiet (DDC)
510 Mathematik
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Local-global principle, Diophantine definability, PRC
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ISO 690FEHM, Arno, 2013. Elementary geometric local-global principles for fields. In: Annals of Pure and Applied Logic. 2013, 164(10), pp. 989-1008. ISSN 0168-0072. eISSN 0168-0072. Available under: doi: 10.1016/j.apal.2013.05.003
BibTex
@article{Fehm2013Eleme-23511,
  year={2013},
  doi={10.1016/j.apal.2013.05.003},
  title={Elementary geometric local-global principles for fields},
  number={10},
  volume={164},
  issn={0168-0072},
  journal={Annals of Pure and Applied Logic},
  pages={989--1008},
  author={Fehm, Arno}
}
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