König's theorem (set theory)

König's theorem is an important result in set theory and combinatorial set theory, specifically related to the study of infinite trees. The theorem states the following: If \( T \) is an infinite tree of finite height such that every node in \( T \) has a finite number of children, then \( T \) has either: 1. An infinite branch (a path through the tree that visits infinitely many nodes), or 2.