Quasi-o-minimal structures

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


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



    Upload a copy of this work     Papers currently archived: 94,678

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Quasi-O-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Essentially periodic ordered groups.Françoise Point & Frank O. Wagner - 2000 - Annals of Pure and Applied Logic 105 (1-3):261-291.
A monotonicity theorem for dp-minimal densely ordered groups.John Goodrick - 2010 - Journal of Symbolic Logic 75 (1):221-238.
Locally o-Minimal Structures with Tame Topological Properties.Masato Fujita - 2023 - Journal of Symbolic Logic 88 (1):219-241.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
Expansions of o-Minimal Structures by Iteration Sequences.Chris Miller & James Tyne - 2006 - Notre Dame Journal of Formal Logic 47 (1):93-99.
Definable sets in Boolean ordered o-minimal structures. II.Roman Wencel - 2003 - Journal of Symbolic Logic 68 (1):35-51.


Added to PP

305 (#71,700)

6 months
39 (#112,817)

Historical graph of downloads
How can I increase my downloads?