Results 51 to 60 of about 199 (115)
The Strong and Super Tree Property at Successors of Singular Cardinals
, 2023 The strong tree property and ITP (also called the super tree property) are generalizations of the tree property that characterize strong compactness and supercompactness up to inaccessibility.
Adkisson, William
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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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, 1998 We construct a model in which there are no ℵn-Aronszajn trees for any finiten⩾2, starting from a model with infinitely many supercompact cardinals.
Foreman, Matthew, Cummings, James
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Maximality and ontology: how axiom content varies across philosophical frameworks. [PDF]
Synthese, 2020 Barton N, Friedman SD.
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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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Higher Structural Reflection and Very Large Cardinals [PDF]
Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2023-2024. Tutor: Joan Bagaria PigrauOne line of research in set theory aims at deriving large cardinal axioms from strengthened forms of ...
Hou, Nai-Chung
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REFLECTION OF STATIONARY SETS AND THE TREE PROPERTY AT THE SUCCESSOR OF A SINGULAR CARDINAL
, 2017 International audienceAbstract We show that from infinitely many supercompact cardinals one can force a model of ZFC where both the tree property and the stationary reflection hold at א ω 2 +1
Fontanella, Laura, Magidor, Menachem
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Chang's conjecture may fail at supercompact cardinals (submitted)
, 2006 We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(κ^+,κ)\notcc(\aleph\_1,\aleph\_0)$ when $κ$ is supercompact. The actual proofs show that $ω\_1$-regressive Kurepa-trees are consistent above a supercompact cardinal even though ${\rm MM}$ destroys
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Contributions to the theory of Large Cardinals through the method of Forcing [PDF]
, 2020 [eng] The present dissertation is a contribution to the field of Mathematical Logic and, more particularly, to the subfield of Set Theory. Within Set theory, we are mainly concerned with the interactions between the largecardinal axioms and the method of
Poveda Ruzafa, Alejandro
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A FRAMEWORK FOR FORCING CONSTRUCTIONS AT SUCCESSORS OF SINGULAR CARDINALS
, 2013 . We describe a framework for proving consistency results about singular cardinals of arbitrary co nality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular cardinal κ of ...
Mirna Dšamonja +5 more
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