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Kurepa trees and Namba forcing

Published online by Cambridge University Press:  12 March 2014

Bernhard König
Affiliation:
Graduate School of Information Science, Nagoya University, Furocho, Chikusa-Ku, Nagoya 464-8601, Japan, E-mail: bkoenig.smtp@gmail.com
Yasuo Yoshinobu
Affiliation:
Graduate School of Information Science, Nagoya University, Furocho, Chikusa-Ku, Nagoya 464-8601, Japan, E-mail: bkoenig.smtp@gmail.com

Abstract

We show that strongly compact cardinals and 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 requires a non-standard application of MM. As a corollary, we find a consistent example of an ω2-closed poset that is not forcing equivalent to any ω2-directed-closed poset.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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