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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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##### References:
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