Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces

Peter J. Nyikos — 2003

Fundamenta Mathematicae

Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of countably compact...

A non-metrizable collectionwise Hausdorff tree with no uncountable chains and no Aronszajn subtrees

Akira IwasaPeter J. Nyikos — 2006

Commentationes Mathematicae Universitatis Carolinae

It is independent of the usual (ZFC) axioms of set theory whether every collectionwise 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.

Page 1

Download Results (CSV)