Klimiashvili, Alexander Algebraic function fields and non-standard analysis. (English) Zbl 1346.03052 Bull. Georgian Natl. Acad. Sci. (N.S.) 9, No. 2, 27-32 (2015). Summary: Non-standard analysis was developed in 1960–1970 as an application of logical methods to such topic as abstract algebra, analysis field theory. The present work considers applications of non-standard analysis to modern algebra. It is based on A. Robinson’s work [in: Contribution to non-standard analysis. London: North-Holland Publishing Company. 1–14 (1972; Zbl 0247.12107)]. A possibility of generalizing Robinson’s argument is considered. Some other applications of non-standard analysis to algebra include, for example, applications of non-standard methods, computational group theory and the theory of rewrite rules. MSC: 03H05 Nonstandard models in mathematics 12L15 Nonstandard arithmetic and field theory 14H05 Algebraic functions and function fields in algebraic geometry Keywords:non-standard analysis; algebraic field theory; group theory Citations:Zbl 0247.12107 PDFBibTeX XMLCite \textit{A. Klimiashvili}, Bull. Georgian Natl. Acad. Sci. (N.S.) 9, No. 2, 27--32 (2015; Zbl 1346.03052) Full Text: Link