The special Aronszajn tree property at $\aleph_2$ and $GCH$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866911850639130624 |
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| author | Asperó, David Golshani, Mohammad |
| author_facet | Asperó, David Golshani, Mohammad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_07638 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The special Aronszajn tree property at $\aleph_2$ and $GCH$ Asperó, David Golshani, Mohammad Logic 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. |
| title | The special Aronszajn tree property at $\aleph_2$ and $GCH$ |
| topic | Logic |
| url | https://arxiv.org/abs/1809.07638 |