Editing Tree (set theory) (section)

{{Short description|Concept in set theory, a topic in mathematics}}
{{for|other notions of tree in set theory|Tree (descriptive set theory)|Tree (disambiguation)}}
{{no footnotes|date=January 2021}}
[[File:Infinite set-theoretic tree.png|thumb|A branch (highlighted green) of a set-theoretic tree. Here dots represent elements, arrows represent the order relation, and [[ellipsis|ellipses]] and dashed arrows represent (possibly infinite) un-pictured elements and relationships.]]

In [[set theory]], a '''tree''' is a [[partially ordered set]] <math>(T,<)</math> such that for each <math>t\in T</math>, the set <math>\{s\in T: s<t\}</math> is [[well-ordered]] by the relation <math><</math>. 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.