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The super tree property at the successor of a singular

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Abstract

For an inaccessible cardinal κ, the super tree property (ITP) at κ holds if and only if κ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor of the limit of ω many supercompact cardinals. Then we show that it can consistently hold at ℵω+1. We also consider a stronger principle, ISP and certain weaker variations of it. We determine which level of ISP can hold at a successor of a singular. These results fit in the broad program of testing how much compactness can exist in the universe, and obtaining large cardinal-type properties at smaller cardinals.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago, Chicago, IL, 60613, USA

    Sherwood Hachtman & Dima Sinapova

Authors
  1. Sherwood Hachtman
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  2. Dima Sinapova
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Corresponding author

Correspondence to Dima Sinapova.

Additional information

Hachtman was partially supported through the National Science Foundation, grant DMS-1246844.

Sinapova was partially supported by the National Science Foundation, grant Career-1454945.

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Hachtman, S., Sinapova, D. The super tree property at the successor of a singular. Isr. J. Math. 236, 473–500 (2020). https://doi.org/10.1007/s11856-020-2000-5

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  • DOI: https://doi.org/10.1007/s11856-020-2000-5

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