Results 1 to 10 of about 92 (75)
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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On the partition property of measures on Pℋλ
International Journal of Mathematics and Mathematical Sciences, 1982 The partition property for measures on Pℋλ was formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4].
Donald H. Pelletier
doaj +2 more sources
Epireflections and supercompact cardinals
Journal of Pure and Applied Algebra, 2009 15 ...
Joan Bagaria, Carles Casacuberta
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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)
exaly +4 more sources
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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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 Wholeness Axioms and the Class of Supercompact Cardinals
Bulletin of the Polish Academy of Sciences Mathematics, 2012 We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.
Arthur W Apter
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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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Flipping properties and supercompact cardinals [PDF]
Fundamenta Mathematicae, 1980 Di Prisco, Carlos A. +1 more
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