A characterization of lifting generics for Sacks-like forcings
Radek Honzík (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Radek Honzík (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Keith Devlin (1975)
Fundamenta Mathematicae
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Adam Figura (1981)
Fundamenta Mathematicae
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Sy-David Friedman (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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Sy-David Friedman (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Kurepa, Đuro (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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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...
Krister Segerberg (1974)
Fundamenta Mathematicae
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Arthur Apter (1984)
Fundamenta Mathematicae
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Spasojević, Z. (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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Dima Sinapova (2015)
Fundamenta Mathematicae
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We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.