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Indestructibility, instances of strong compactness, and level by level inequivalence

✍ Scribed by Arthur W. Apter

Publisher
Springer
Year
2010
Tongue
English
Weight
294 KB
Volume
49
Category
Article
ISSN
0933-5846

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πŸ“œ SIMILAR VOLUMES

Indestructibility and level by level equ
Indestructibility and level by level equivalence and inequivalence
✍ Arthur W. Apter πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 133 KB

If ΞΊ < Ξ» are such that ΞΊ is indestructibly supercompact and Ξ» is 2 Ξ» supercompact, it is known from [4] that {Ξ΄ < ΞΊ | Ξ΄ is a measurable cardinal which is not a limit of measurable cardinals and Ξ΄ violates level by level equivalence between strong compactness and supercompactness} must be unbounded i

Level by level equivalence and strong co
Level by level equivalence and strong compactness
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## Abstract We force and construct models in which there are non‐supercompact strongly compact cardinals which aren't measurable limits of strongly compact cardinals and in which level by level equivalence between strong compactness and supercompactness holds non‐trivially except at strongly compac

Failures of GCH and the level by level e
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✍ Arthur W. Apter πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 175 KB

## Abstract We force and obtain three models in which level by level equivalence between strong compactness and supercompactness holds and in which, below the least supercompact cardinal, GCH fails unboundedly often. In two of these models, GCH fails on a set having measure 1 with respect to certai

Supercompactness and measurable limits o
Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence
✍ Arthur W. Apter πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 125 KB

## Abstract We construct models for the level by level equivalence between strong compactness and supercompactness in which for __ΞΊ__ the least supercompact cardinal and __Ξ΄__ ≀ __ΞΊ__ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2^__Ξ΄__^ > __Ξ΄__ ^+^ and