Submission date: 24 February 2020

Abstract:

Bès and Choffrut recently showed that there are no intermediate structures between (ℝ,<,+) and (ℝ,<,+,ℤ). We prove a generalization: if R is an o-minimal expansion of (ℝ,<,+) by bounded subsets of Euclidean space then there are no intermediate structures between R and (R,ℤ). It follows there are no intermediate structures between (ℝ,<,+,sin|_{[0,2π]}) and (ℝ,<,+,sin).

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Full text arXiv 2002.10508: pdf, ps.