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Expansions of o-minimal structures by fast sequences

Published online by Cambridge University Press:  12 March 2014

Harvey Friedman  and
Chris Miller
Harvey Friedman
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue Columbus, Ohio 43210, USA, E-mail: [email protected], URL: www.math.ohio-state.edu/~friedman
Chris Miller
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue Columbus, Ohio 43210., USA, E-mail: [email protected], URL: http://www.math.ohio-state.edu/~miller
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Abstract

Let ℝ be an o-minimal expansion of (ℝ, <, +) and (ϕ k )kЄℕ be a sequence of positive real numbers such that limtk →+∞ f (ϕ k )/ϕ k +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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 410 - 418
Copyright
Copyright © Association for Symbolic Logic 2005

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