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Preprint Number 379
379. Vincent Guingona, Joseph Flenner
Canonical forests in directed families
Submission date: 11 November 2011.
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.
Mathematics Subject Classification: 06A07, 03C45
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