Submission date: 2 February 2016.

Abstract:

We construct a class of finite rank multiplicative subgroups of the complex numbers such that the expansion of the real field by such a group is model-theoretically well-behaved. As an application we show that a classification of expansions of the real field by cyclic multiplicative subgroups of the complex numbers due to Hieronymi does not even extend to expansions by subgroups with two generators.

Mathematics Subject Classification:

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Full text arXiv 1602.01142: pdf, ps.