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Thorn independence in the field of real numbers with a small multiplicative group. (English) Zbl 1171.03020
Building on results of L. van den Dries and A. Günaydin in [“The fields of real and complex numbers with a small multiplicative group”, Proc. Lond. Math. Soc. (3) 93, No. 1, 43–81 (2006; Zbl 1101.03028)], the authors investigate the model theory of pairs \((R, G)\) where \(R\) is a real closed field, and \(G\) is a dense multiplicative subgroup of \(R^{>0}\) with the Mann property and such that for each prime number \(p\), the subgroup of the \(p\)th powers in \(G\) has finite index in \(G\). Among others, they show that such structures are super-rosy and eliminate imaginaries up to codes for small sets.

MSC:
03C60 Model-theoretic algebra
03C64 Model theory of ordered structures; o-minimality
12L12 Model theory of fields
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