PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 38(52), pp. 711 (1985) 

A TREE AXIOMDjuro KurepaMatematicki fakultet, Beograd, YugoslaviaAbstract: 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. Full text of the article:
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