Canonical forests in directed families

Joseph Flenner; Vincent Guingona

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arXiv · 1111.2843

Canonical forests in directed families

Joseph Flenner·Vincent Guingona

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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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Joseph Flenner, Vincent Guingona. 2011-11-11. Canonical forests in directed families. https://arxiv.org/abs/1111.2843

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