TY - JOUR

T1 - Defining the set of integers in expansions of the real field by a closed discrete set

AU - Hieronymi, Philipp

PY - 2010/6

Y1 - 2010/6

N2 - Let D ⊆ ℝ be closed and discrete and f : Dn → R be such that f (Dn) is somewhere dense. We show that (ℝ, +,-,f) defines ℤ.As an application, we get that for every α, β ∈ ℝ> o with logα (β) ℚ, the real field expanded by the two cyclic multiplicative subgroups generated by α and β defines ℤ.

AB - Let D ⊆ ℝ be closed and discrete and f : Dn → R be such that f (Dn) is somewhere dense. We show that (ℝ, +,-,f) defines ℤ.As an application, we get that for every α, β ∈ ℝ> o with logα (β) ℚ, the real field expanded by the two cyclic multiplicative subgroups generated by α and β defines ℤ.

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U2 - 10.1090/S0002-9939-10-10268-8

DO - 10.1090/S0002-9939-10-10268-8

M3 - Article

AN - SCOPUS:77951190950

SN - 0002-9939

VL - 138

SP - 2163

EP - 2168

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -