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Hypergraphs and proper forcing
Journal of Mathematical Logic 19 (2):1950007 (2019)
Abstract
Given a Polish space X and a countable collection of analytic hypergraphs on X, I consider the σ-ideal generated by Borel anticliques for the hypergraphs in the family. It turns out that many of the quotient posets are proper. I investigate the forcing properties of these posets, certain natural operations on them, and prove some related dichotomies.Other Versions
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Citations of this work
Subadditive families of hypergraphs.Jindřich Zapletal - forthcoming - Annals of Pure and Applied Logic.
References found in this work
Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
Continuous Ramsey theory on polish spaces and covering the plane by functions.Stefan Geschke, Martin Goldstern & Menachem Kojman - 2004 - Journal of Mathematical Logic 4 (2):109-145.
Analytic countably splitting families.Otmar Spinas - 2004 - Journal of Symbolic Logic 69 (1):101-117.
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