![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Infinite_set-theoretic_tree.png/640px-Infinite_set-theoretic_tree.png&w=640&q=50)
Tree (set theory)
From Wikipedia, the free encyclopedia
For other notions of tree in set theory, see Tree (descriptive set theory) and Tree (disambiguation).
In set theory, a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. minimal element), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees.
![]() | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (January 2021) |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Infinite_set-theoretic_tree.png/640px-Infinite_set-theoretic_tree.png)