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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic stability, forking, and þ-forking


Authors: Darío García, Alf Onshuus and Alexander Usvyatsov
Journal: Trans. Amer. Math. Soc. 365 (2013), 1-22
MSC (2010): Primary 03C45, 03C07
Published electronically: July 24, 2012
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Abstract: Abstract notions of ``smallness'' are among the most important tools that model theory offers for the analysis of arbitrary structures. The two most useful notions of this kind are forking (which is closely related to certain measure zero ideals) and thorn-forking (which generalizes the usual topological dimension). Under certain mild assumptions, forking is the finest notion of smallness, whereas thorn-forking is the coarsest.

In this paper we study forking and thorn-forking, restricting ourselves to the class of generically stable types. Our main conclusion is that in this context these two notions coincide. We explore some applications of this equivalence.


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Additional Information

Darío García
Affiliation: Departamento de Matemáticas, Universidade de los Andes, Cra 1 No. 18A-10, Edificio H, Bogotá, 111711, Colombia

Alf Onshuus
Affiliation: Departamento de Matemáticas, Universidade de los Andes, Cra 1 No. 18A-10, Edificio H, Bogotá, 111711, Colombia

Alexander Usvyatsov
Affiliation: Centro de Matemática e Aplicacões Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto,2, 1649-003 Lisboa, Portugal

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05451-1
PII: S 0002-9947(2012)05451-1
Received by editor(s): February 2, 2010
Received by editor(s) in revised form: August 24, 2010
Published electronically: July 24, 2012
Additional Notes: This paper was written while the second author was a visiting professor at Oxford University and Queen Mary University of London
The third author was partially supported by FCT grant SFRH/BPD/34893/2007
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.