A weakly compact cardinal (WCC) is a certain type of large cardinal with many equivalent definitions, such as this one: Let \([x]^2\) be all the 2-element subsets of \(x\). Then an uncountable cardinal \(\alpha\) is weakly compact if and only if, for every function \(f: [\alpha]^2 \mapsto \{0, 1\}\), there is a set \(S \subseteq \alpha\) such that \(|S| = \alpha\) and \(f\) maps every member of \([S]^2\) to either all 0 or all 1. More intuitively, any two-coloring of the edges of the complete graph \(K_\alpha\) contains a monochromatic \(K_\alpha\) as a subgraph.