Submission date: 28 June 2009.

Abstract:

Abstract. Let D\subseteq R be closed and discrete and f : D^n \to R be such that f(D^n ) is somewhere dense. We show that (R, +, ·, f ) defines Z. As an application, we get that for every α, β in R with log_α (β) \notin Q, the real field expanded by the two cyclic multiplicative subgroups generated by α and β defines Z.

Mathematics Subject Classification: 03C64

Keywords and phrases:

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