English

Canonical forests in directed families

Logic 2011-11-29 v2

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.

Cite

@article{arxiv.1111.2843,
  title  = {Canonical forests in directed families},
  author = {Joseph Flenner and Vincent Guingona},
  journal= {arXiv preprint arXiv:1111.2843},
  year   = {2011}
}

Comments

12 pages, 2 figures

R2 v1 2026-06-21T19:34:56.661Z