
TL;DR
This paper establishes a maximal version of a coloring property in set theory by proving a specific partition relation involving regular cardinals and their successors.
Contribution
It introduces a new maximal coloring property $Pr_1$ for successor cardinals under certain regularity conditions.
Findings
Proves $Pr_1(oldsymbol{ extcolor{red}{ ext{lambda}}},oldsymbol{ extcolor{red}{ ext{lambda}}},oldsymbol{ extcolor{red}{ ext{lambda}}},oldsymbol{ extcolor{red}{ heta}})$ for regular cardinals $ heta< ext{lambda}= ext{partial}^+$.
Establishes maximal coloring properties for successors of regular cardinals.
Contributes to the understanding of partition relations in set theory.
Abstract
We get a quite maximal version of the colouring property by proving when are regular cardinals.
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