Independence results | Trees (set theory)

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 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 -Aronszajn trees). They are named for Nachman Aronszajn, who constructed an Aronszajn tree in 1934; his construction was described by . 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). (Wikipedia).

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Assaf Rinot : Distributive Aronszajn trees

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From playlist Logic and Foundations

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From playlist Guide to Trees & Plants

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From playlist Logic and Foundations

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From playlist Guide to Trees & Plants

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From playlist Introduction to Algorithms

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From playlist 3D printing

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CMSA Combinatorics Seminar, 27 October 2020

From playlist CMSA Combinatorics Seminar

Related pages

Kurepa tree | Kőnig's lemma | Nachman Aronszajn | Proper forcing axiom | Set theory | Η set | Club set | Cardinal number | Continuum hypothesis | Weakly compact cardinal | Aronszajn line | First uncountable ordinal | Inaccessible cardinal | Tree (set theory) | Suslin tree | Martin's axiom