论文标题
奇异红衣主教的Halpern--läuchli定理和弱版本的失败
The Halpern--Läuchli Theorem at singular cardinals and failures of weak versions
论文作者
论文摘要
本文继续对无数枢机主教的Halpern--Läuchli定理进行了调查。 We prove in ZFC that the Halpern--Läuchli Theorem for one tree of height $κ$ holds whenever $κ$ is strongly inaccessible and the coloring takes less than $κ$ colors. We prove consistency of the Halpern--Läuchli Theorem for finitely many trees of height $κ$, where $κ$ is a strong limit cardinal of countable cofinality. On the other hand, we prove failure of weak forms of Halpern--\Lauchli\ for trees of height $κ$, whenever $κ$ is a strongly inaccessible, non-Mahlo cardinal or a singular strong limit cardinal with cofinality the successor of a regular cardinal.我们还证明，对于所有强烈无法访问，非紧凑的红衣主教的薄弱版本的$ L $。
This paper continues a line of investigation of the Halpern--Läuchli Theorem at uncountable cardinals. We prove in ZFC that the Halpern--Läuchli Theorem for one tree of height $κ$ holds whenever $κ$ is strongly inaccessible and the coloring takes less than $κ$ colors. We prove consistency of the Halpern--Läuchli Theorem for finitely many trees of height $κ$, where $κ$ is a strong limit cardinal of countable cofinality. On the other hand, we prove failure of weak forms of Halpern--\Lauchli\ for trees of height $κ$, whenever $κ$ is a strongly inaccessible, non-Mahlo cardinal or a singular strong limit cardinal with cofinality the successor of a regular cardinal. We also prove failure in $L$ of a weak version for all strongly inaccessible, non-weakly compact cardinals.
