Entangled Suslin lines and OGA
Carlos Martinez-Ranero, Lucas Polymeris
TL;DR
This paper constructs a model demonstrating the existence of a 2-entangled Suslin line under the Open Graph Axiom, resolving longstanding questions about the structure and separability of such lines.
Contribution
It introduces a model where a 2-entangled Suslin line exists without any separable 2-entangled uncountable linear order, answering open problems in set theory.
Findings
Existence of a 2-entangled Suslin line in the model
Existence of a 2-entangled uncountable linear order that is not separable
Resolution of a problem posed by Carroy, Levine, and Notaro
Abstract
We construct a model of the Open Graph Axiom (OGA) in which there is a 2-entangled Suslin line . Consequently, in this model, there is a 2-entangled uncountable linear order, but no such order is separable. This resolves a problem posed by Carroy, Levine, and Notaro \cite{carroy2025} and answers a question from McKenney on MathOverflow \cite{Mckenney2014}.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Logic, programming, and type systems