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arXiv · 1708.00528

Club isomorphisms on higher Aronszajn trees

John Krueger
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Abstract

We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed $\omega_2$-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal $\omega_1$-Aronszajn trees are club isomorphic, which follows from $\textsf{PFA}$. The statement that any two normal countably closed $\omega_2$-Aronszajn trees are club isomorphic implies that there are no $\omega_2$-Suslin trees, so our proof also expands on the method of Laver-Shelah for obtaining the $\omega_2$-Suslin hypothesis.

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John Krueger. 2017-08-01. Club isomorphisms on higher Aronszajn trees. https://arxiv.org/abs/1708.00528

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