THE INEFFABLE TREE PROPERTY and FAILURE of the SINGULAR CARDINALS HYPOTHESIS

James Cummings; Yair Hayut; Menachem Magidor; Itay Neeman; Dima Sinapova; Spencer

doi:10.1090/tran/8110

THE INEFFABLE TREE PROPERTY and FAILURE of the SINGULAR CARDINALS HYPOTHESIS

James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

ITP is a combinatorial principle that is a strengthening of the tree property. For an inaccessible cardinal κ, ITP at κ holds if and only if κ is supercompact. And just like the tree property, it can be forced to hold at accessible cardinals. A broad project is obtaining ITP at many cardinals simultaneously. Past a singular cardinal, this requires failure of SCH.We prove that from large cardinals, it is consistent to have failure of SCH at κ together with ITP κ+. Then we bring down the result to κ = ? ω2 .

Original language	English
Pages (from-to)	5937-5955
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	8
DOIs	https://doi.org/10.1090/tran/8110
State	Published - Aug 2020

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THE INEFFABLE TREE PROPERTY and FAILURE of the SINGULAR CARDINALS HYPOTHESIS

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