On the weak Borel chromatic number and cardinal invariants of the continuum

2023/02/20 by Poór, Márk, Shelah, Saharon
#FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2302.10141

Abstract

We prove that consistently, cov(M)< λ₀ < λ₁ < λ_∞ < 2^ℵ₀, where λ₀ denotes the weak Borel chromatic number of the Kechris-Solecki-Todorčević graph \mathbbG₀, that is, the minimal cardinality of a \mathbbG₀-independent Borel covering of 2^ω, while λ₁ and λ_∞ are the corresponding invariants of the graph \mathbbG₁ and the simple graph associated with the equivalence relation E₀.

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