Geodesic
A Tree Axiom
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 7
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In connection with my previous results from 1935, and results of other mathematicians (Tarski, Erdös, Hanf, Keisler, Baumgartger$\ldots $) the following Tree (or Dendrity) Axiom is formulated: For any regular uncountable ordinal $n$ there exists a tree An of height (rank) $n$ such that $|X| |n|$ for every level $X$ as well as for every subchain $X$ of An. In other words, the following assertion Dn holds: There exists a tree $T$ such that for every regular ordinal $n>\omega_0$ the conditions (2:0), (2:1), (2:2) hold. 
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     author = {{\DJ}uro Kurepa},
     title = {A {Tree} {Axiom}},
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Đuro Kurepa. A Tree Axiom. Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 7 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a1/