### Expansions of o-Minimal Structures by Iteration Sequences

Chris Miller and James Tyne
Source: Notre Dame J. Formal Logic Volume 47, Number 1 (2006), 93-99.

#### Abstract

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.

First Page:
Primary Subjects: 03C64
Secondary Subjects: 06F15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1143468314
Digital Object Identifier: doi:10.1305/ndjfl/1143468314
Mathematical Reviews number (MathSciNet): MR2211185
Zentralblatt MATH identifier: 1107.03040

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