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June 2005 Expansions of o-minimal structures by fast sequences
Harvey Friedman, Chris Miller
J. Symbolic Logic 70(2): 410-418 (June 2005). DOI: 10.2178/jsl/1120224720

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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Harvey Friedman. Chris Miller. "Expansions of o-minimal structures by fast sequences." J. Symbolic Logic 70 (2) 410 - 418, June 2005. https://doi.org/10.2178/jsl/1120224720

Information

Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1089.03031
MathSciNet: MR2140038
Digital Object Identifier: 10.2178/jsl/1120224720

Subjects:
Primary: 03C64

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 2 • June 2005
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