Expansions of O-Minimal Structures by Fast Sequences
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→+∝ ƒ(ϕk)/ϕk+1 = 0 for every ƒ: 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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