2021/04/30 by Assaf Rinot, Jing Zhang, Rinot, Assaf +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.2104.15031
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arxiv created 2021/04/30 · arxiv updated 2021/05/03
We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest conceivable transformations. Along the way, we obtain new results on Shelah's coloring principle Pr1. For κ inaccessible, we prove the consistency of Pr1(κ,κ,κ,κ). For successors of regulars, we obtain a full lifting of Galvin's 1980 theorem. In contrast, the full lifting of Galvin's theorem to successors of singulars is shown to be inconsistent.