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

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

2009-06-26

arxiv.org/abs/0906.4972v2

Proc. Amer. Math. Soc. 138 (2010) 2163-2168

Mathematics

Logic

to appear Proc. Amer. Math. Soc

Scientific paper

Let D\subseteq \mathbb{R} be closed and discrete and f:D^n \to \mathbb{R} be such that f(D^n) is somewhere dense. We show that (\mathbb{R},+,\cdot,f) defines the set of integers. As an application, we get that for every a,b \in \mathbb{R} with \log_{a}(b)\notin \mathbb{Q}, the real field expanded by the two cyclic multiplicative subgroups generated by a and b defines the set of integers.

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