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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
