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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 .

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  • 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). (en)
  • En mathématiques, et plus précisément en théorie des ensembles, un arbre d'Aronszajn est un arbre non dénombrable n'ayant que des branches dénombrables et que des niveaux dénombrables. Nachman Aronszajn construisit en 1934 le premier arbre ayant cette propriété. (fr)
  • 集合論におけるアロンシャイン木(あろんしゃいんき、英: Aronszajn tree)とは、非可算な木で非可算なレベルを持たず、非可算な枝も持たないもののことである。例えば、ススリン木はアロンシャイン木である。一般化すると、基数κに対して、κ-アロンシャイン木とは、高さκの木で全てのレベルのサイズがκ未満で、全ての枝の高さがκ未満の木のこと(すなわち、単にアロンシャイン木と言えば -アロンシャイン木のことである)。1934年にこの木を構成したナフマン・アロンシャインの名に因む。 κ-アロンシャイン木が存在しない基数κはtree propertyを持っているという。(κが正則でありかつ非可算であるという条件も含まれているとする場合もある。) (ja)
  • Uma árvore de Aronszajn (especificamente, uma árvore ω1-Aronszajn) é uma árvore incontável sem níveis incontáveis e sem ramos incontáveis. (pt)
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  • Ch. (en)
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  • Aronszajn_tree (en)
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  • Schlindwein (en)
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  • Aronszajn tree (en)
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  • En mathématiques, et plus précisément en théorie des ensembles, un arbre d'Aronszajn est un arbre non dénombrable n'ayant que des branches dénombrables et que des niveaux dénombrables. Nachman Aronszajn construisit en 1934 le premier arbre ayant cette propriété. (fr)
  • 集合論におけるアロンシャイン木(あろんしゃいんき、英: Aronszajn tree)とは、非可算な木で非可算なレベルを持たず、非可算な枝も持たないもののことである。例えば、ススリン木はアロンシャイン木である。一般化すると、基数κに対して、κ-アロンシャイン木とは、高さκの木で全てのレベルのサイズがκ未満で、全ての枝の高さがκ未満の木のこと(すなわち、単にアロンシャイン木と言えば -アロンシャイン木のことである)。1934年にこの木を構成したナフマン・アロンシャインの名に因む。 κ-アロンシャイン木が存在しない基数κはtree propertyを持っているという。(κが正則でありかつ非可算であるという条件も含まれているとする場合もある。) (ja)
  • Uma árvore de Aronszajn (especificamente, uma árvore ω1-Aronszajn) é uma árvore incontável sem níveis incontáveis e sem ramos incontáveis. (pt)
  • 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 . (en)
rdfs:label
  • Aronszajn tree (en)
  • Arbre d'Aronszajn (fr)
  • アロンシャイン木 (ja)
  • Árvore de Aronszajn (pt)
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