Tree (descriptive set theory)

In descriptive set theory, a tree on a set X {\displaystyle X} is a collection of finite sequences of elements of X {\displaystyle X} such that every prefix of a sequence in the collection also belongs to the collection. == Definitions == === Trees === The collection of all finite sequences of elements of a set X {\displaystyle X} is denoted X < ω {\displaystyle X^{<\omega }} .