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December 2012 Kurepa trees and Namba forcing
Bernhard König, Yasuo Yoshinobu
J. Symbolic Logic 77(4): 1281-1290 (December 2012). DOI: 10.2178/jsl.7704130

Abstract

We show that strongly compact cardinals and 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 requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.

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Bernhard König. Yasuo Yoshinobu. "Kurepa trees and Namba forcing." J. Symbolic Logic 77 (4) 1281 - 1290, December 2012. https://doi.org/10.2178/jsl.7704130

Information

Published: December 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1270.03095
MathSciNet: MR3051626
Digital Object Identifier: 10.2178/jsl.7704130

Subjects:
Primary: 03E40, 03E55

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 4 • December 2012
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