Tree (set theory)とは 意味・読み方・使い方

In set theory, a tree is a partially ordered set (poset) (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. For each t ∈ T, the order type of {s ∈ T : s < t} is called the height of t (denoted ht(t, T)). The height of T itself is the least ordinal greater than the height of each element of T. A root of a tree T is an element of height 0. Frequently trees are assumed to have only one root (as the typical questions that are investigated in this field are easily reduced to questions about single-rooted trees).