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arXiv · 1809.07638

The special Aronszajn tree property at $\aleph_2$ and $GCH$

David Asperó·Mohammad Golshani
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Abstract

Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which $GCH$ holds and all $\aleph_2$-Aronszajn trees are special and hence there are no $\aleph_2$-Souslin trees. This result answers a well-known open question from the 1970's.

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David Asperó, Mohammad Golshani. 2018-09-20. The special Aronszajn tree property at $\aleph_2$ and $GCH$. https://arxiv.org/abs/1809.07638

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