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Canonical forests in directed families


Authors: Joseph Flenner and Vincent Guingona
Journal: Proc. Amer. Math. Soc. 142 (2014), 1849-1860
MSC (2010): Primary 06A07, 03C45
DOI: https://doi.org/10.1090/S0002-9939-2014-11935-6
Published electronically: February 26, 2014
MathSciNet review: 3182006
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Abstract: Two uniqueness results on representations of sets constructible in a directed family of sets are given. In the unpackable case, swiss cheese decompositions are unique. In the packable case, they are not unique but admit a quasi-ordering under which the minimal decomposition is unique. Both cases lead to a one-dimensional elimination of imaginaries in VC-minimal and quasi-VC-minimal theories.


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Additional Information

Joseph Flenner
Affiliation: Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics, University of Saint Francis, 2701 Spring Street, Fort Wayne, Indiana 46808
Email: jflenner@sf.edu

Vincent Guingona
Affiliation: Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame, Indiana 46556
Email: guingona.1@nd.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11935-6
Keywords: Directed family of sets, swiss cheese decomposition, VC-minimality, elimination of imaginaries
Received by editor(s): November 10, 2011
Received by editor(s) in revised form: June 29, 2012
Published electronically: February 26, 2014
Additional Notes: Both authors were supported by NSF grant DMS-0838506.
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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