Hypergraphs and proper forcing

Journal of Mathematical Logic 19 (2):1950007 (2019)
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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.

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10.1142/s0219061319500077

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Citations of this work

Terminal notions.Jindřich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (4):470-478.
Subadditive families of hypergraphs.Jindřich Zapletal - forthcoming - Annals of Pure and Applied Logic.

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References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
Analytic countably splitting families.Otmar Spinas - 2004 - Journal of Symbolic Logic 69 (1):101-117.
N–localization property.Andrzej Rosłanowski - 2006 - Journal of Symbolic Logic 71 (3):881 - 902.

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