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Kurepa-trees and Namba-forcing

Bernhard Koenig·Yasuo Yoshinobu
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Abstract

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

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Bernhard Koenig, Yasuo Yoshinobu. 2006-05-04. Kurepa-trees and Namba-forcing. https://arxiv.org/abs/math/0605130

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