Results 191 to 200 of about 793 (236)

Condensation and large cardinals

Fundamenta Mathematicae, 2011
Wir definieren lokale Clubmengenkondensation (Local Club Condensation), ein Prinzip, welches Eigenschaften von Godels Kondensationsprinzip isoliert und verallgemeinert. Wir zeigen, dass wir uber einem beliebigen Modell der Mengenlehre durch die Erzwingungsmethode zu einem Modell der Mengenlehre gelangen konnen, welches lokale Clubmengenkondensation ...
Friedman, Sy-David, Holy, Peter
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Virtual large cardinals

Annals of Pure and Applied Logic, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victoria Gitman, Ralf Schindler
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LARGE CARDINALS BEYOND CHOICE

The Bulletin of Symbolic Logic, 2019
AbstractThe HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V (in the sense that it correctly computes successors of singular cardinals greater than δ) or HOD is “far” from V (in the sense that all regular cardinals greater than or equal to δ are measurable in HOD).
Joan Bagaria, Peter Koellner, W. Hugh Woodin   +2 more
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GENERICITY AND LARGE CARDINALS

Journal of Mathematical Logic, 2005
We lift Jensen's coding method into the context of Woodin cardinals. By a theorem of Woodin, any real which preserves a "strong witness" to Woodinness is set-generic. We show however that there are class-generic reals which are not set-generic but preserve Woodinness, using "weak witnesses".
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Large cardinals and large dilators

Journal of Symbolic Logic, 1998
AbstractApplying Woodin's non-stationary tower notion of forcing, I prove that the existence of a supercompact cardinal κ in V and a Ramsey dilator in some small forcing extension V[G] implies the existence in V of a measurable dilator of size κ, measurable by κ-complete measures.
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Are Large Cardinal Axioms Restrictive?

Philosophia Mathematica, 2023
AbstractThe independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim.
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Combinatorics on large cardinals

Journal of Symbolic Logic, 1992
Our framework is ZFC, and we view cardinals as initial ordinals. Baumgartner ([Bal] and [Ba2]) studied properties of large cardinals by considering these properties as properties of normal ideals and not as properties of cardinals alone. In this paper we study these combinatorial properties by defining operations which take as input one or more ideals ...
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Large Cardinals and Ramifiability for Directed Sets [PDF]

MLQ, 2000
Notions usually defined for cardinals, such as regularity, ramifiability, and measurability, are defined and studied in the context of directed posets. In this setting, it is proved that measurability implies ramifiability, and strong compactness for cardinals is characterized in terms of ramifiability for directed posets. An analogous characterization
Esser, Olivier, Hinnion, Roland
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Inner Models and Large Cardinals

Bulletin of Symbolic Logic, 1995
In this paper, we sketch the development of two important themes of modern set theory, both of which can be regarded as growing out of work of Kurt Gödel. We begin with a review of some basic
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On large cardinals and partition relations

Journal of Symbolic Logic, 1971
A significant portion of the study of large cardinals in set theory centers around the concept of “partition relation”. To best capture the basic idea here, we introduce the following notation: for x and y sets, κ an infinite cardinal, and γ an ordinal less than κ, we let [x]γ denote the collection of subsets of x of order-type γ and abbreviate with ...
E. M. Kleinberg, Richard A. Shore
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