Canonical forests in directed families
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- by Joseph Flenner and Vincent Guingona PDF
- Proc. Amer. Math. Soc. 142 (2014), 1849-1860 Request permission
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.References
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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
- MR Author ID: 942387
- Email: guingona.1@nd.edu
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3182006