THE INEFFABLE TREE PROPERTY and FAILURE of the SINGULAR CARDINALS HYPOTHESIS

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

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)5937-5955
Number of pages19
JournalTransactions of the American Mathematical Society
Volume373
Issue number8
DOIs
StatePublished - Aug 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society. All rights reserved.

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