Journal of Symbolic Logic

Expansions of o-minimal structures by fast sequences

Harvey Friedman and Chris Miller

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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.

Article information

Source
J. Symbolic Logic Volume 70, Issue 2 (2005), 410-418.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1120224720

Digital Object Identifier
doi:10.2178/jsl/1120224720

Mathematical Reviews number (MathSciNet)
MR2140038

Zentralblatt MATH identifier
1089.03031

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality

Citation

Friedman, Harvey; Miller, Chris. Expansions of o-minimal structures by fast sequences. Journal of Symbolic Logic 70 (2005), no. 2, 410--418. doi:10.2178/jsl/1120224720. http://projecteuclid.org/euclid.jsl/1120224720.


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