Source: J. Symbolic Logic
Volume 70, Issue 2
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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