Sealed Kurepa Trees
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914626076147712 |
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| author | Giron, Itamar Hayut, Yair |
| author_facet | Giron, Itamar Hayut, Yair |
| contents | In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing cardinals. On the other hand, we derive a proper forcing notion for making an arbitrary Kurepa tree into a non-distributive tree without collapsing $\aleph_1$ and $\aleph_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00572 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sealed Kurepa Trees Giron, Itamar Hayut, Yair Logic 03E05 03E35 In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing cardinals. On the other hand, we derive a proper forcing notion for making an arbitrary Kurepa tree into a non-distributive tree without collapsing $\aleph_1$ and $\aleph_2$. |
| title | Sealed Kurepa Trees |
| topic | Logic 03E05 03E35 |
| url | https://arxiv.org/abs/2401.00572 |