Questions tagged [infinitary-combinatorics]

For topics of a combinatorial character in set theory. Topics belonging to "combinatorial set theory" may be tagged this way. These include: Partition calculus, diamond principles, square principles, combinatorial properties of infinite graphs or partial orders, etc.

This tag is for topics of a combinatorial character studied in set theory. Topics belonging to "combinatorial set theory" or "infinitary combinatorics" may be tagged this way. These include: Partition calculus (generalizations of Ramsey theory to infinite cardinals, infinite ordinals, other partially ordered structures, etc), diamond ($\diamondsuit$) principles and relatives (such as $\clubsuit$), square ($\Box$) principles, club-guessing principles, combinatorial properties of infinite graphs or partial orders (such as their chromatic number, marriage problems, etc), among others.

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Can the Infinite Ramsey Theorem be extended even when coloring a graph's edges with an infinite number of colors?

In the language of partition calculus, I want to know if the following is true: Let $n$ be an integer, $n \geq 2$. Then $\aleph_n \rightarrow (\aleph_0)^2_{\aleph_0}$. I'm new to infinitary combinatorics, and it's possible that I used the wrong…
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