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Preprint Number 1576
1576. Erik Walsberg Coarse dimension and definable sets in expansions of the ordered real
vector space E-mail: 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: Keywords and phrases: |

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