Submission date: 2 March 2019

Abstract:

Suppose E ⊆ ℝ is nowhere dense. If (ℝ,<,+,(x → λ x)_{λ ∈ ℝ}, E) does not define every compact subset of every ℝ^n then for every s > 0 we have |{ k ∈ ℤ, -m ≤ k ≤ m - 1 : [k,k+1] ∩ E ≠ ∅ }| < m^s for all sufficiently large m ∈ ℕ.

Mathematics Subject Classification:

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Full text arXiv 1903.00736: pdf, ps.