Expansions of o-minimal structures by fast sequences

Abstract

AbstractLet ℝ be an o-minimal expansion of (ℝ, <, +) and (ϕk)kЄℕbe a sequence of positive real numbers such that limtk→+∞f(ϕk)/ϕk+1 = 0 for everyf: 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. whereSranges over all subsets of cartesian powers of the range ofϕ.