Submission date: 11 November 2011.

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.

Mathematics Subject Classification: 06A07, 03C45

Keywords and phrases:

Full text arXiv 1111.2843: pdf, ps.