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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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Weak Covering at Large Cardinals
Mathematical Logic Quarterly, 1997AbstractWe show that weakly compact cardinals are the smallest large cardinals k where k+ < k+ is impossible provided 0# does not exist. We also show that if k+Kc < k+ for some k being weakly compact (where Kc is the countably complete core model below one strong cardinal), then there is a transitive set M with M ⊨ ZFC + “there is a strong ...
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Superstrong and other large cardinals are never Laver indestructible
Archive for Mathematical Logic, 2015 Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong cardinals ...
Joan Bagaria +2 more
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Determinacy Axioms and Large Cardinals
, 2023 The study of inner models was initiated by Gödel’s analysis of the constructible universe. Later, the study of canonical inner models with large cardinals, e.g., measurable cardinals, strong cardinals or Woodin cardinals, was pioneered by Jensen ...
Müller, Sandra; orcid:
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Condensation and large cardinals
Fundamenta Mathematicae, 2011Wir 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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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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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victoria Gitman, Ralf Schindler
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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 +2 more
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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 +2 more
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GENERICITY AND LARGE CARDINALS
Journal of Mathematical Logic, 2005We 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, 1998AbstractApplying 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, 2023AbstractThe 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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