Heinemann, Bernhard; Prestel, Alexander Fields regularly closed with respect to finitely many valuations and orderings. (English) Zbl 0566.03023 Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 60, 20-59 (1984). 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 Cited in 5 Documents MSC: 12J10 Valued fields 12J15 Ordered fields 03C60 Model-theoretic algebra 12L12 Model theory of fields Keywords:regularly closed fields; local-global-principle for rational points; irreducible K-varieties; local fields; model completeness Citations:Zbl 0523.12024 PDFBibTeX XMLCite \textit{B. Heinemann} and \textit{A. Prestel}, Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 60, 20--59 (1984; Zbl 0566.03023)