On ℵ0-categorical weakly o-minimal structures

Annals of Pure and Applied Logic 101 (1):65-93 (1999)
  Copy   BIBTEX


0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry



    Upload a copy of this work     Papers currently archived: 92,100

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

A Note on Weakly O-Minimal Structures and Definable Completeness.Alfred Dolich - 2007 - Notre Dame Journal of Formal Logic 48 (2):281-292.
Weakly o-minimal structures and some of their properties.B. Sh Kulpeshov - 1998 - Journal of Symbolic Logic 63 (4):1511-1528.
On ℵ0‐categorical weakly circularly minimal structures.Beibut Sh Kulpeshov - 2006 - Mathematical Logic Quarterly 52 (6):555-574.
Strongly and co-strongly minimal abelian structures.Ehud Hrushovski & James Loveys - 2010 - Journal of Symbolic Logic 75 (2):442-458.
Weakly one-based geometric theories.Alexander Berenstein & Evgueni Vassiliev - 2012 - Journal of Symbolic Logic 77 (2):392-422.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
T-Height in Weakly O-Minimal Structures.James Tyne - 2006 - Journal of Symbolic Logic 71 (3):747 - 762.
The geometry of weakly minimal types.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1044-1053.


Added to PP

41 (#389,432)

6 months
7 (#435,412)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Notes on local o‐minimality.Carlo Toffalori & Kathryn Vozoris - 2009 - Mathematical Logic Quarterly 55 (6):617-632.
Vaught's conjecture for quite o-minimal theories.B. Sh Kulpeshov & S. V. Sudoplatov - 2017 - Annals of Pure and Applied Logic 168 (1):129-149.
On o-amorphous sets.P. Creed & J. K. Truss - 2000 - Annals of Pure and Applied Logic 101 (2-3):185-226.
Criterion for binarity of ℵ 0 -categorical weakly o-minimal theories.B. Sh Kulpeshov - 2007 - Annals of Pure and Applied Logic 145 (3):354-367.

View all 11 citations / Add more citations

References found in this work

Elimination of quantifiers for ordered valuation rings.M. A. Dickmann - 1987 - Journal of Symbolic Logic 52 (1):116-128.

Add more references