van den Dries, Lou; Günaydin, Ayhan The fields of real and complex numbers with a small multiplicative group. (English) Zbl 1101.03028 Proc. Lond. Math. Soc. (3) 93, No. 1, 43-81 (2006). Summary: We consider the model theory of the real and complex fields with a multiplicative group having the Mann property. Among these groups are the finitely generated multiplicative groups in these fields. As a by-product we obtain some results on groups with the Mann property in rings of Witt vectors and in fields of positive characteristic. Cited in 1 ReviewCited in 41 Documents MSC: 03C60 Model-theoretic algebra 13K05 Witt vectors and related rings (MSC2000) 12D99 Real and complex fields 03C10 Quantifier elimination, model completeness, and related topics 03C35 Categoricity and completeness of theories 03C64 Model theory of ordered structures; o-minimality 03C98 Applications of model theory 12L12 Model theory of fields 13L05 Applications of logic to commutative algebra Keywords:field of real numbers; field of complex numbers; model theory; multiplicative group; Mann property; rings of Witt vectors; fields of positive characteristic PDFBibTeX XMLCite \textit{L. van den Dries} and \textit{A. Günaydin}, Proc. Lond. Math. Soc. (3) 93, No. 1, 43--81 (2006; Zbl 1101.03028) Full Text: DOI