Results 1 to 10 of about 78 (68)
Supercompact cardinals, sets of reals, and weakly homogeneous trees [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1988 It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of L (R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA
Woodin WH.
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The Hypothesis and a supercompact cardinal
Mathematical Logic Quarterly, 2017 AbstractIn this paper, we prove that: if κ is supercompact and the Hypothesis holds, then there is a proper class of regular cardinals in which are measurable in . Woodin also proved this result independently . As a corollary, we prove Woodin's Local Universality Theorem.
Yong Cheng
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The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $${\theta}$$ θ -supercompact [PDF]
Archive for Mathematical Logic, 2015 We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly $θ$-supercompact, for any desired $θ$. In addition, we prove several global results showing how the entire class of weakly compact cardinals, a proper class, can be made to coincide with the class of unfoldable ...
Brent Cody +2 more
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Strong compactness, measurability, and the class of supercompact cardinals [PDF]
Fundamenta Mathematicae, 2001 In this paper, the author continues the investigation of the possible interplays of supercompactness, strong compactness and measurability. The author shows how to achieve simultaneously the following three properties when designing forcing extensions: (1) preserve the supercompactness of all those supercompact cardinals which are limits of ...
Arthur W Apter
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Exactly controlling the non-supercompact strongly compact cardinals [PDF]
Journal of Symbolic Logic, 2003 AbstractWe summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension.
Arthur W. Apter, Joel David Hamkins
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Epireflections and supercompact cardinals
Journal of Pure and Applied Algebra, 2009 15 ...
Bagaria, Joan +2 more
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Combinatorial characterization of supercompact cardinals [PDF]
Proceedings of the American Mathematical Society, 1974 It is proved that supercompact cardinals can be characterized by combinatorial properties which are generalizations of ineffability.
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The large cardinals between supercompact and almost-huge [PDF]
Archive for Mathematical Logic, 2015 I analyze the hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal. Many of these cardinals are defined by modifying the definition of a high-jump cardinal. A high-jump cardinal is defined as the critical point of an elementary embedding $j: V \to M$ such that $M$ is closed under sequences of length $\sup\set{j(f)(κ)
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Generically supercompact cardinals by forcing with chain conditions
, 2022 A ccc-generically supercompact cardinal $κ$ can be smaller than or equal to the continuum. On the other hand, such a cardinal $κ$ still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically measurable cardinals (Theorem 4.1).
Fuchino, Sakaé, Sakai, Hiroshi
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Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics
Bulletin of Symbolic Logic, 2008 The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing ...
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