Strongest transformations

DOI10.1007/S00493-023-00011-0arXiv2104.15031OpenAlexW3157699003MaRDI QIDQ6081159

Publication date: 4 October 2023

Published in: Combinatorica (Search for Journal in Brave)

Abstract: 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

P r_{1}

. For

k a p p a

inaccessible, we prove the consistency of

P r_{1} (k a p p a, k a p p a, k a p p a, k a p p a)

. 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.

Full work available at URL: https://arxiv.org/abs/2104.15031

zbMATH Keywords

square stick xbox strong colorings proxy principle walks on ordinals transformations of the transfinite plane

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05) Partition relations (03E02)