A Non-Metrizable Collectionwise Hausdorff Tree with No Uncountable Chains and Aronszajn Subtrees
It is independent of the usual (ZFC) axioms of set theory whether every collec- tionwise Hausdorff tree is either metrizable or has an uncountable chain. We show that even if we add “or has an Aronszajn subtree,” the statement remains ZFC-independent. This is done by constructing a tree as in the title, using the set-theoretic hypothesis ♦∗, which holds in Gödel’s Constructible Universe.
Published in Commentaciones Mathematicae Universitatis Carolinae, Volume 47, Issue 3, 2006, pages 515-523.
© Commentationes Mathmaticae Universitatis Carolinae (CMUC) 2006, Charles University, Prague.