AI 中文总结
该研究引入含知名大基数概念的紧性基数分层，通过其刻画弱紧等大基数，并得到新紧性基数大小的下界。
AI 中文摘要
我们研究了关于使用无穷多颜色的列表着色（一种特定形式的图着色）的紧性性质。我们引入了一种新的紧性基数分层，其中也包含一些公认的大基数概念，并利用它证明了各类大基数（包括弱紧基数、强紧基数和δ-强紧基数）可通过列表着色的紧性来刻画。我们还获得了新引入的紧性基数大小的下界。
英文摘要
We investigate compactness properties with respect to list colouring, a certain form of graph colouring, with infinitely many colours. We introduce a new hierarchy of compactness cardinals, that also includes some well-established large cardinal notions, and use it to show that various types of large cardinals, including weakly compact, strongly compact, and $δ$-strongly compact cardinals, can be characterized in terms of compactness for list colouring. We also obtain lower bounds on the size of our newly introduced compactness cardinals.
