A Partition Theorem for Pairs of Finite Sets

Thomas Jech, Saharon Shelah
1991 Journal of The American Mathematical Society  
Every partition of [[ω 1 ] <ω ] 2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite character.
doi:10.2307/2939283 fatcat:v2fv75oloffuzpdeceikqtswbm