 Graham–Rothschild theorem

The Graham–Rothschild theorem is a result in set theory, particularly in the area of infinite combinatorics. It deals with the properties of certain kinds of partitions of the natural numbers, specifically the partition relations involving sequences and subsets. The theorem states the following: If a family of sets of natural numbers (or more generally, a collection of sets) has a certain property related to partitioning, then it must contain subsets that exhibit a specific structure.