Results 91 to 100 of about 199 (115)

Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence

Mathematical Logic Quarterly, 2006
AbstractWe construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2δ > δ + and δ is < 2δ supercompact.
Arthur W Apter
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Supercompact cardinals and trees of normal ultrafilters

Journal of Symbolic Logic, 1982
Supercompact cardinals are usually defined in terms of the existence of certain normal ultrafilters. It is well known that there is a natural partial ordering on the collection of all normal ultrafilters associated with a super-compact cardinal, that of normal ultrafilter restriction. Using this notion, we define a tree structure T on the collection of
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Supercompactness and measurable limits of strong cardinals

Journal of Symbolic Logic, 2001
AbstractIn this paper, two theorems concerning measurable limits of strong cardinals and supercompactness are proven. This generalizes earlier work, both individual and joint with Shelah.
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There are many normal ultrafiltres corresponding to a supercompact cardinal

Israel Journal of Mathematics, 1971
It is proved that ifκ is supercompact, there are at least (2• P κ(β)•)+normal ultrafilters overP k (β) and ifV=H.O.D. exactly (22• P κ(β)•) normal ultrafilters.
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Supercompact cardinals, elementary embeddings and fixed points

Journal of Symbolic Logic, 1982
Supercompactness is usually defined in terms of the existence of certain ultrafilters. By the well-known procedure of taking ultrapowers of V (the universe of sets) and transitive collapses, one obtains transitive inner models of V and corresponding elementary embeddings from V into these inner models.
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Some structural results concerning supercompact cardinals

Journal of Symbolic Logic, 2001
Abstract.We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ+ supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals.
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On a combinatorial property of menas related to the partition property for measures on supercompact cardinals

Journal of Symbolic Logic, 1983
AbstractT.K. Menas [4, pp. 225–234] introduced a combinatorial property Χ(μ) of a measure μ on a supercompact cardinal κ and proved that measures with this property also have the partition property. We prove here that Menas' property is not equivalent to the partition property.
Kenneth Kunen, Donald H. Pelletier
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Supercompact cardinals, trees of normal ultrafilters, and the partition property

Journal of Symbolic Logic, 1986
AbstractSuppose κ is a supercompact cardinal. It is known that for every λ ≥ κ, many normal ultrafilters on Pκ(λ) have the partition property. It is also known that certain large cardinal assumptions imply the existence of normal ultrafilters without the partition property. In [1], we introduced the tree T of normal ultrafilters associated with κ.
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The κ-closed unbounded filter and supercpmpact cardinals

Journal of Symbolic Logic, 1981
The consistency of the Axiom of Determinateness (AD) poses a somewhat problematic question for set theorists. On the one hand, many mathematicians have studied AD, and none has yet derived a contradiction. Moreover, the consequences of AD which have been proven form an extensive and beautiful theory.
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7 The least supercompact cardinal

2022
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