Notre Dame Journal of Formal Logic

Expansions of o-Minimal Structures by Iteration Sequences

Chris Miller and James Tyne


Let P be the ω-orbit of a point under a unary function definable in an o-minimal expansion ℜ of a densely ordered group. If P is monotonically cofinal in the group, and the compositional iterates of the function are cofinal at +\infty in the unary functions definable in ℜ, then the expansion (ℜ, P) has a number of good properties, in particular, every unary set definable in any elementarily equivalent structure is a disjoint union of open intervals and finitely many discrete sets.

Article information

Notre Dame J. Formal Logic, Volume 47, Number 1 (2006), 93-99.

First available in Project Euclid: 27 March 2006

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 06F15: Ordered groups [See also 20F60]

o-minimal d-minimal densely ordered group


Miller, Chris; Tyne, James. Expansions of o-Minimal Structures by Iteration Sequences. Notre Dame J. Formal Logic 47 (2006), no. 1, 93--99. doi:10.1305/ndjfl/1143468314.

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