Journal of Symbolic Logic 65 (3):1115-1132 (2000)

Abstract
A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1
Keywords Quasi-O-Minimal Theory   O-Minimal Theory   Ordered Group   Theory of U -Rank 1
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DOI 10.2307/2586690
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References found in this work BETA

An Introduction to Stability Theory.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (2):465-467.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.

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Citations of this work BETA

Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
Presburger Sets and P-Minimal Fields.Raf Cluckers - 2003 - Journal of Symbolic Logic 68 (1):153-162.
Coset-Minimal Groups.Oleg Belegradek, Viktor Verbovskiy & Frank O. Wagner - 2003 - Annals of Pure and Applied Logic 121 (2-3):113-143.
Essentially Periodic Ordered Groups.Françoise Point & Frank O. Wagner - 2000 - Annals of Pure and Applied Logic 105 (1-3):261-291.

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