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Kurepa trees and Namba forcing

  • Bernhard König (a1) and Yasuo Yoshinobu (a1)

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.

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Keywords

Kurepa trees and Namba forcing

  • Bernhard König (a1) and Yasuo Yoshinobu (a1)

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