 Ramsey’s Theorems themselves have yielded numerous important applications, generalizations and concepts in other branches of mathematics. For example the notion of a Ramsey Cardinal, \(\kappa\), where we require that for a set \(X\) of cardinality \(\kappa\) and any partition of the finite subsets of \(\kappa\) into two sets there is a subset \(Y\) of \(X\), also of cardinality \(\kappa\), such that any two finite subsets of \(Y\) of the same size are in the same part of the partition. Ramsey Cardinals were one of the first examples of large cardinals, a central area of research in Set Theory. One feature of such cardinals is that they are so large that their existence cannot be proved within ZFC.