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Journal of the London Mathematical Society
Article . 2024 . Peer-reviewed
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Article . 2024
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https://dx.doi.org/10.48550/ar...
Article . 2023
License: arXiv Non-Exclusive Distribution
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Transferring compactness

Authors: Tom Benhamou; Jing Zhang;

Transferring compactness

Abstract

AbstractWe demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of large cardinals, we construct a model of set theory in which there is a strongly inaccessible cardinal that is ‐‐stationary for all but not weakly compact. This is in sharp contrast to the situation in the constructible universe , where being ‐‐stationary is equivalent to being ‐indescribable. We also show that it is consistent that there is a cardinal such that is ‐stationary for all and , answering a question of Sakai.

Keywords

Large cardinals, FOS: Mathematics, Consistency and independence results, Mathematics - Logic, Partition relations, Logic (math.LO)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
hybrid