Aronszajn tree

In set theory, a tree of uncountable height with no uncountable branches and no uncountable levels

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.

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Aronszajn tree

In set theory, a tree of uncountable height with no uncountable branches and no uncountable levels

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.

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From Wikipedia

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 cardinal κ, a κ-Aronszajn tree is a tree of height κ in which all levels have size less than κ and all branches have height less than κ (so Aronszajn trees are the same as ℵ 1 {\displaystyle \aleph _{1}} -Aronszajn trees). They are named for Nachman Aronszajn, who constructed an Aronszajn tree in 1934; his construction was described by Kurepa (1935). A cardinal κ for which no κ-Aronszajn trees exist is said to have the tree property (sometimes the condition that κ is regular and uncountable is included).

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