Expansions of o-Minimal Structures by Iteration Sequences

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
Keywords o-minimal   d-minimal   densely ordered group
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DOI 10.1305/ndjfl/1143468314
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James Tyne (2006). T-Height in Weakly O-Minimal Structures. Journal of Symbolic Logic 71 (3):747 - 762.

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