A minimal Kurepa tree with respect to club embeddings
Volume 245 / 2019
Fundamenta Mathematicae 245 (2019), 293-304
MSC: Primary 03E05.
DOI: 10.4064/fm593-6-2018
Published online: 8 February 2019
Abstract
We show it is consistent with $\mathrm {GCH}$ that there is a minimal Kurepa tree with respect to club embeddings. That is, there is a Kurepa tree $T$ which club embeds in all of its Kurepa subtrees in the sense of Abraham and Shelah (1985). Moreover, the Kurepa tree we introduce has no Aronszajn subtree.
