Journal of Symbolic Logic 70 (2):410-418 (2005)

Abstract
Let ℜ be an o-minimal expansion of (ℝ, <+) and (φk)k∈ℕ be a sequence of positive real numbers such that limk→+∞f(φk)/φk+1=0 for every f:ℝ→ ℝ definable in ℜ. (Such sequences always exist under some reasonable extra assumptions on ℜ, in particular, if ℜ is exponentially bounded or if the language is countable.) Then (ℜ, (S)) is d-minimal, where S ranges over all subsets of cartesian powers of the range of φ
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DOI 10.2178/jsl/1120224720
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References found in this work BETA

Expansions of the Real Field with Power Functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.
Expansions of o-Minimal Structures by Iteration Sequences.Chris Miller & James Tyne - 2006 - Notre Dame Journal of Formal Logic 47 (1):93-99.

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Uniform Bounds on Growth in o-Minimal Structures.Janak Ramakrishnan - 2010 - Mathematical Logic Quarterly 56 (4):406-408.

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