Results 61 to 70 of about 218 (121)
On Extensions of Supercompactness
, 2020 We show that, in terms of both implication and consistency strength, an extendible with a larger strong cardinal is stronger than an enhanced supercompact, which is itself stronger than a hypercompact, which is itself weaker than an extendible.
Norman Lewis Perlmutter +1 more
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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
openaire +2 more sources
On the consistency strength of the proper forcing axiom
, 2011 In recent work, the second author extended combinatorial principles due to Jech and Magidor that characterize certain large cardinal properties so that they can also hold true for small cardinals.
Christoph Weiß +3 more
core +1 more source
Compact Spaces, Compact Cardinals, and Elementary Submodels
, 2002 If M is an elementary submodel and X a topological space, then XM denotes the set X \M given the topology generated by the open subsets of X which are members of M . Call a compact space squashable iff for some M , XM is compact and XM 6= X. The first
Kenneth Kunen, Kunen, Kenneth
core +1 more source
Definable tree property for uncountable regular cardinals
, 2023 The primary goal of this paper is to establish a model of $ZFC$ wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with the utilization of both a supercompact cardinal and a measurable cardinal ...
Golshani, Mohammad, Mirabi, Mostafa
core
, 2019 The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal.
Goldberg, Gabriel
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A framework for forcing constructions at successors of singular cardinals
, 2018 We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular cardinal κ of ...
Mirna Dzamonja (5364554) +4 more
core +1 more source
The Proper Forcing Axiom (PFA) represents a significant strengthening of Martin's Axiom, asserting the existence of generic filters for a broad class of proper partial orders. This monograph investigates the consistency strength of PFA, situating it within the hierarchy of large cardinals.
Revista, Zen, MFC, 10
openaire +2 more sources
The first measurable can be the first inaccessible cardinal
In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(κ)\geq2$.
Karagila, Asaf, Hayut, Yair, Gitik, Moti
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Force to change large cardinal strength
, 2015 This dissertation includes many theorems which show how to change large cardinal properties with forcing. I consider in detail the degrees of inaccessible cardinals (an analogue of the classical degrees of Mahlo cardinals) and provide new large cardinal ...
Carmody, Erin Kathryn
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