Geodesic
A Tree Axiom
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 7 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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/