Stable generic structures


Authors
Abstract
Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. In particular, the generic structure need not be ω-saturated and so the argument for stability is significantly more complicated. We further show that these structures are “flat” and do not interpret a group
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/0168-0072(95)00027-5
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,711
Through your library

References found in this work BETA

A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
ℵ0-Categorical, ℵ0-Stable Structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
On Generic Structures.D. W. Kueker & M. C. Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (2):175-183.
The Primal Framework I.J. T. Baldwin & S. Shelah - 1990 - Annals of Pure and Applied Logic 46 (3):235-264.

View all 6 references / Add more references

Citations of this work BETA

ℵ0-Categorical Structures with a Predimension.David M. Evans - 2002 - Annals of Pure and Applied Logic 116 (1-3):157-186.
Model Completeness of the New Strongly Minimal Sets.Kitty L. Holland - 1999 - Journal of Symbolic Logic 64 (3):946-962.
Constructing Ω-Stable Structures: Model Completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.

View all 24 citations / Add more citations

Similar books and articles

Ab Initio Generic Structures Which Are Superstable but Not Ω-Stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1-2):203-211.
Ages of Expansions of Ω-Categorical Structures.A. Ivanov & K. Majcher - 2007 - Notre Dame Journal of Formal Logic 48 (3):371-380.
Subgroups of Stable Groups.Frank Wagner - 1990 - Journal of Symbolic Logic 55 (1):151-156.
On Superstable Generic Structures.Koichiro Ikeda & Hirotaka Kikyo - 2012 - Archive for Mathematical Logic 51 (5-6):591-600.
CM-Triviality and Generic Structures.Ikuo Yoneda - 2003 - Archive for Mathematical Logic 42 (5):423-433.
The Stable Core.Sy-David Friedman - 2012 - Bulletin of Symbolic Logic 18 (2):261-267.
The Stable Forking Conjecture and Generic Structures.Massoud Pourmahdian - 2003 - Archive for Mathematical Logic 42 (5):415-421.
Small Stable Groups and Generics.Frank O. Wagner - 1991 - Journal of Symbolic Logic 56 (3):1026-1037.
Stable Definability and Generic Relations.Byunghan Kim & Rahim Moosa - 2007 - Journal of Symbolic Logic 72 (4):1163 - 1176.
Stable Types in Rosy Theories.Assaf Hasson & Alf Onshuus - 2010 - Journal of Symbolic Logic 75 (4):1211-1230.
Automorphisms of Homogeneous Structures.A. Ivanov - 2005 - Notre Dame Journal of Formal Logic 46 (4):419-424.
DOP and FCP in Generic Structures.John T. Baldwin & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (2):427-438.

Analytics

Added to PP index
2014-01-16

Total views
4 ( #1,010,518 of 2,328,174 )

Recent downloads (6 months)
3 ( #545,313 of 2,328,174 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature