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

 

Additivity of the dp-rank


Authors: Itay Kaplan, Alf Onshuus and Alexander Usvyatsov
Journal: Trans. Amer. Math. Soc. 365 (2013), 5783-5804
MSC (2010): Primary 03C45, 03C98; Secondary 05D99, 68R05
Published electronically: July 1, 2013
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Abstract: The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types, and we discuss the possible relations between dp-rank and VC-density.


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Additional Information

Itay Kaplan
Affiliation: Mathematischen Instituts, Universität Münster, Einsteinstraße 62, 48149 Münster, Germany

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

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05782-0
PII: S 0002-9947(2013)05782-0
Keywords: Dp-rank, dp-minimality, VC-density
Received by editor(s): September 7, 2011
Received by editor(s) in revised form: December 21, 2011
Published electronically: July 1, 2013
Additional Notes: The third author was supported by FCT grant SFRH/BPD/34893/2007 and FCT research project PTDC/MAT/101740/2008.
We thank the organizers of the meeting “Model theory: Around Valued Fields and Dependent Theories” at Oberwolfach in January 2010. Special thanks to Sergei Starchenko for valuable discussions during and after the meeting. We would also like to thank John Goodrick, Alfred Dolich, Pierre Simon and the anonymous referee for some very helpful remarks and comments on earlier drafts of this paper.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.