Tree (set theory)

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In set theory, a tree is a partially ordered set ${\displaystyle (T,<)}$ such that for each ${\displaystyle t\in T}$, the set ${\displaystyle \{s\in T:s<t\}}$ is well-ordered by the relation ${\displaystyle <}$. 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.