Results 51 to 60 of about 218 (121)
, 1983 Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω2 or ω3.
Abraham, Uri
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Flipping properties and supercompact cardinals [PDF]
Fundamenta Mathematicae, 1980 Di Prisco, Carlos A. +1 more
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Successors of singular cardinals and measurability
, 1985 It is shown, starting from a model in which κ < λ, κ is 2λ supercompact, and λ is a measurable cardinal, how to force and obtain a model in which the Axiom of Choice is false and in which the successor of a singular cardinal is ...
Apter, Arthur W, Arthur W Apter
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PFA and the definability of the nonstationary ideal
, 2023 We produce, relative to a ${\sf ZFC}$ model with a supercompact cardinal, a ${\sf ZFC}$ model of the Proper Forcing Axiom in which the nonstationary ideal on $\omega_1$ is $\Pi_1$-definable in a parameter from $H_{\aleph_2}$
Schindler, Ralf +3 more
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Maximality and ontology: how axiom content varies across philosophical frameworks. [PDF]
Synthese, 2020 Barton N, Friedman SD.
europepmc +1 more source
The Ultrapower Axiom implies GCH above a supercompact cardinal
, 2018 We prove that the Generalized Continuum Hypothesis holds above a supercompact cardinal assuming the Ultrapower Axiom, an abstract comparison principle motivated by inner model theory at the level of supercompact cardinals.
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On the consistency of local and global versions of Chang’s Conjecture
, 2017 We show that for many pairs of infinite cardinals κ > μ + > μ \kappa > \mu ^+ > \mu , ( κ + ,
Yair Hayut, Monroe Eskew
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The Ultimate L Conjecture and Inner Models for Supercompact Cardinals
The Inner Model Program, initiated by Gödel's construction of L, seeks to provide canonical, fine-structural inner models for large cardinal axioms. While successful up to the level of Woodin cardinals, the program faces a significant barrier at the level of supercompact cardinals due to the complexity of iteration strategies.
Revista, Zen, MFC, 10
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Filter spaces: towards a unified theory of large cardinal and embedding axioms
, 1989 We construct a parametrized framework, at the center of which is a space D and the notion of a fine, normal ultrafilter on that space. The assertion that such a filter exists is a statement of varying power.
Henle, James +7 more
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Epireflections and supercompact cardinals
We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class.
Casacuberta i Vergés, Carles +3 more
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