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Fields regularly closed with respect to finitely many valuations and orderings. (English) Zbl 0566.03023

We introduce and investigate a class of fields \(K\) which satisfy a local-global-principle for rational points on absolutely irreducible \(K\)-varieties referring to a finite number of ’local fields’. The algebraically maximal among such fields satisfy a local-global-principle for ’model completeness’. This approach generalizes L. P. D. van den Dries’ [Model theory of fields. Decidability and bounds for polynomial ideals. Thesis, Utrecht (1978)] as well as Yu. L. Ershov’s [Usp. Mat. Nauk 37, No. 3(225), 55–93 (1982; Zbl 0523.12024)].
Reviewer: Bernhard Heinemann

MSC:

12J10 Valued fields
12J15 Ordered fields
03C60 Model-theoretic algebra
12L12 Model theory of fields

Citations:

Zbl 0523.12024
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