Kurepa's hypothesis and the continuum
Keith Devlin (1975)
Fundamenta Mathematicae
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Keith Devlin (1975)
Fundamenta Mathematicae
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Adam Figura (1981)
Fundamenta Mathematicae
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Krister Segerberg (1974)
Fundamenta Mathematicae
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A. Wojciechowska (1972)
Fundamenta Mathematicae
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W. Hanf (1964)
Fundamenta Mathematicae
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Uri Abraham, Saharon Shelah, R. Solovay (1987)
Fundamenta Mathematicae
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James Cummings (2010)
Open Mathematics
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Answering a question raised by Luis Pereira, we show that a continuous tree-like scale can exist above a supercompact cardinal. We also show that the existence of a continuous tree-like scale at ℵω is consistent with Martin’s Maximum.
Kurepa, Đuro (1985)
Publications de l'Institut Mathématique. Nouvelle Série
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Erik Ellentuck (1966)
Fundamenta Mathematicae
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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...
Sy-David Friedman, Víctor Torres-Pérez (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo...
Julius Barbanel (1985)
Fundamenta Mathematicae
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