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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Generic stability, forking, and þ-forking
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by Darío García, Alf Onshuus and Alexander Usvyatsov PDF
Trans. Amer. Math. Soc. 365 (2013), 1-22 Request permission

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
  • MR Author ID: 780610
  • ORCID: setImmediate$0.6870641344914623$6
  • Alexander Usvyatsov
  • Affiliation: Centro de Matemática e Aplicacões Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto,2, 1649-003 Lisboa, Portugal
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 1-22
  • MSC (2010): Primary 03C45, 03C07
  • DOI: https://doi.org/10.1090/S0002-9947-2012-05451-1
  • MathSciNet review: 2984050