Displaying similar documents to “Representation Theorem for Minimal σ -Algebras”

The consistency strength of the tree property at the double successor of a measurable cardina

Natasha Dobrinen, Sy-David Friedman (2010)

Fundamenta Mathematicae

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The Main Theorem is the equiconsistency of the following two statements: (1) κ is a measurable cardinal and the tree property holds at κ⁺⁺; (2) κ is a weakly compact hypermeasurable cardinal. From the proof of the Main Theorem, two internal consistency results follow: If there is a weakly compact hypermeasurable cardinal and a measurable cardinal far enough above it, then there is an inner model in which there is a proper class of measurable cardinals, and in which the tree property...