TL;DR
This paper explores the properties of certain proper forcing notions derived from analytic hypergraphs on Polish spaces, focusing on their forcing behavior, operations, and related combinatorial principles.
Contribution
It introduces a new class of proper forcing posets generated by hypergraphs and simplifies their analysis using combinatorial hypergraph considerations.
Findings
Many quotient posets are proper.
Forcing properties can be analyzed via hypergraph combinatorics.
Fusion and iteration arguments are simplified through hypergraph techniques.
Abstract
Given a Polish space X and a countable family of analytic hypergraphs on X, I consider the sigma-ideal generated by Borel sets which are anticliques in at least one hypergraph 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. For this broad class of posets, most fusion arguments and iteration preservation arguments can be replaced with simple combinatorial considerations concerning the hypergraphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.