# Category: Trees (set theory)

Kurepa tree
In set theory, a Kurepa tree is a tree (T, <) of height ω1, each of whose levels is at most countable, and has at least ℵ2 many branches. This concept was introduced by Kurepa. The existence of a Kure
Aronszajn tree
In set theory, an Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn tree. More generally, for a card
Milliken's tree theorem
In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting ro
Morass (set theory)
In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create "large" structures from a "small" number of "small" approximations. They were invent
Tree (descriptive set theory)
In descriptive set theory, a tree on a set is a collection of finite sequences of elements of such that every prefix of a sequence in the collection also belongs to the collection.
Cantor tree
In mathematical set theory, the Cantor tree is either the full binary tree of height ω + 1, or a topological space related to this by joining its points with intervals, that was introduced by Robert L
Suslin tree
In mathematics, a Suslin tree is a tree of height ω1 such thatevery branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn
Jech–Kunen tree
A Jech–Kunen tree is a set-theoretic tree with properties that are incompatible with the generalized continuum hypothesis. It is named after Thomas Jech and Kenneth Kunen, both of whom studied the pos
Halpern–Läuchli theorem
In mathematics, the Halpern–Läuchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for set theory in which the Boolean prime ideal theo
Honest leftmost branch
In set theory, an honest leftmost branch of a tree T on ω × γ is a branch (maximal chain) ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). Here, [T] denotes the set of branche
Stemmatics
No description available.
Tree (set theory)
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. mi
Laver tree
No description available.