Kurepa-trees and Namba-forcing

Bernhard Koenig (1) , Yasuo Yoshinobu (2)

1 ELM - Équipe de Logique Mathématique
2 NAGOYA - Nagoya

We show that compact cardinals and {\rm MM} are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding 'regressive' $\lambda$-Kurepa-trees in either case. We argue that the destruction of regressive Kurepa-trees with {\rm MM} requires the use of Namba forcing.

Domaines: Logique [math.LO]

Bernhard Koenig, Yasuo Yoshinobu. Kurepa-trees and Namba-forcing. 2006. ⟨hal-00023751⟩