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Strong tree properties for small cardinals

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Mar 2013Embargo end date: 01 Jan 2012 France English Publisher:Cambridge University Press (CUP)Journal:The Journal of Symbolic Logic, volume 78, pages 317-333 (issn: 0022-4812, eissn: 1943-5886, Copyright policy )
Authors: Fontanella, Laura;

doi: 10.2178/jsl.7801220 , 10.48550/arxiv.1201.6673

arXiv: 1201.6673

Strong tree properties for small cardinals

Abstract

AbstractAn inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every n ≥ 2 and μ ≥ ℕn, we have (ℕn, μ)-ITP.

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Keywords

large cardinals, Large cardinals, 03E55, forcing, tree property, FOS: Mathematics, [MATH] Mathematics [math], Mathematics - Logic, Logic (math.LO)

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    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.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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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!
8
Average
Top 10%
Average
Green
bronze