Displaying similar documents to “Pressing Down Lemma for λ -trees and its applications”

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

Akira Iwasa, Peter J. Nyikos (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal

Saharon Shelah, R. Jin (1992)

Fundamenta Mathematicae

Similarity:

By an ω 1 - tree we mean a tree of power ω 1 and height ω 1 . Under CH and 2 ω 1 > ω 2 we call an ω 1 -tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between ω 1 and 2 ω 1 . In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus 2 ω 1 > ω 2 that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus 2 ω 1 = ω 4 that there only exist Kurepa trees with ω 3 -many branches, which answers...