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Preprint Number 1142
1142. Gabriel Conant Stability and sparsity in sets of natural numbers E-mail: Submission date: 5 January 2017 Abstract: Given a set A ⊆ N, we consider the relationship between
stability of the structure (Z,+,0,A) and sparsity assumptions on the
set A. We first show that a strong enough sparsity assumption on A yields
stability of (Z,+,0,A). Specifically, if there is a function
f:A → R^+ such that sup_{a\in A}|a-f(a)|<∞
and {s/t : s,t in f(A), ¬ (t ≤ s)} is closed and discrete, then
(Z,+,0,A) is superstable (of U-rank ω if A is infinite). Mathematics Subject Classification: Keywords and phrases: |

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