Archive for Mathematical Logic 53 (1-2):203-210 (2014)

Abstract
We extend the dichotomy between 1-basedness and supersimplicity proved in Shami :309–332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami :309–332, 2011)]. We conclude that every hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the language is countable.
Keywords Simple theory  Forking-topology  Unidimensional theory
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s00153-013-0362-7
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: 50,308
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.
Lovely Pairs of Models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
Some Remarks on One-Basedness.Frank O. Wagner - 2004 - Journal of Symbolic Logic 69 (1):34-38.
Unidimensional Theories Are Superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.

View all 10 references / Add more references

Citations of this work BETA

On the Forking Topology of a Reduct of a Simple Theory.Ziv Shami - 2020 - Archive for Mathematical Logic 59 (3-4):313-324.

Add more citations

Similar books and articles

An Unclassifiable Unidimensional Theory Without OTOP.Ambar Chowdhury & Bradd Hart - 1997 - Notre Dame Journal of Formal Logic 38 (1):93-103.
On Kueker Simple Theories.Ziv Shami - 2005 - Journal of Symbolic Logic 70 (1):216 - 222.
On Countable Simple Unidimensional Theories.Anand Pillay - 2003 - Journal of Symbolic Logic 68 (4):1377-1384.
On the Number of Models of Uncountable Theories.Ambar Chowdhury & Anand Pillay - 1994 - Journal of Symbolic Logic 59 (4):1285-1300.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
On Analyzability in the Forking Topology for Simple Theories.Ziv Shami - 2006 - Annals of Pure and Applied Logic 142 (1):115-124.
Morley Degree in Unidimensional Compact Complex Spaces.Dale Radin - 2006 - Journal of Symbolic Logic 71 (2):569 - 585.
The Classification of Small Weakly Minimal Sets. II.Steven Buechler - 1988 - Journal of Symbolic Logic 53 (2):625-635.
Forking and Dividing in NTP₂ Theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.

Analytics

Added to PP index
2014-01-21

Total views
21 ( #461,931 of 2,326,041 )

Recent downloads (6 months)
5 ( #165,413 of 2,326,041 )

How can I increase my downloads?

Downloads

My notes