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The fields of real and complex numbers with a small multiplicative group. (English) Zbl 1101.03028

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.

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
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