Kurepa trees and Namba forcing

Journal of Symbolic Logic 77 (4):1281-1290 (2012)

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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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
Fragments of Martin's Maximum in Generic Extensions.Y. Yoshinobu & B. Konig - 2004 - Mathematical Logic Quarterly 50 (3):297.

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Citations of this work

Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
Operations, Climbability and the Proper Forcing Axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.
The ⁎-Variation of the Banach–Mazur Game and Forcing Axioms.Yasuo Yoshinobu - 2017 - Annals of Pure and Applied Logic 168 (6):1335-1359.
Preservation Theorems for Namba Forcing.Osvaldo Guzmán, Michael Hrušák & Jindřich Zapletal - 2021 - Annals of Pure and Applied Logic 172 (2):102869.

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