Suslin tree

In mathematics, a Suslin tree is a tree of height ω₁ such that every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin.

Every Suslin tree is an Aronszajn tree.

The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ₁) implies that there are no Suslin trees.

单词	Suslin tree
释义	Suslin tree 英语百科 Suslin tree In mathematics, a Suslin tree is a tree of height ω₁ such that every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ₁) implies that there are no Suslin trees.
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