The super tree property at the successor of a singular

Sherwood Hachtman; Dima Sinapova

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arXiv · 1806.00820

The super tree property at the successor of a singular

Sherwood Hachtman·Dima Sinapova

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Abstract

For an inaccessible cardinal $\kappa$, the super tree property (ITP) at $\kappa$ holds if and only if $\kappa$ 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 $\omega$ many supercompact cardinals. Then we show that it can consistently hold at $\aleph_{\omega+1}$. 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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Sherwood Hachtman, Dima Sinapova. 2018-06-03. The super tree property at the successor of a singular. https://arxiv.org/abs/1806.00820

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