Complicated colorings, revisited

Publication date: 20 February 2022

Abstract: In a paper from 1997, Shelah asked whether

P r_{1} (l a m b d a^{+}, l a m b d a^{+}, l a m b d a^{+}, l a m b d a)

holds for every inaccessible cardinal

l a m b d a

. Here, we prove that an affirmative answer follows from

s q u a r e (l a m b d a^{+})

. Furthermore, we establish that for every pair

c h i < k a p p a

of regular uncountable cardinals,

s q u a r e (k a p p a)

implies

P r_{1} (k a p p a, k a p p a, k a p p a, c h i)

.

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