Constructibility real degrees in the side-by-side Sacks model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912883453984768 |
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| author | Notaro, Lorenzo |
| author_facet | Notaro, Lorenzo |
| contents | We study the join-semilattice of constructibility real degrees in the side-by-side Sacks model, the model of set theory obtained by forcing with a countable-support product of infinitely many Sacks forcings over the constructible universe. In particular, we prove that in the side-by-side Sacks model the join-semilattice of constructibility real degrees is rigid, i.e. it does not have non-trivial automorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructibility real degrees in the side-by-side Sacks model Notaro, Lorenzo Logic Primary 03E35, Secondary 03E45 We study the join-semilattice of constructibility real degrees in the side-by-side Sacks model, the model of set theory obtained by forcing with a countable-support product of infinitely many Sacks forcings over the constructible universe. In particular, we prove that in the side-by-side Sacks model the join-semilattice of constructibility real degrees is rigid, i.e. it does not have non-trivial automorphisms. |
| title | Constructibility real degrees in the side-by-side Sacks model |
| topic | Logic Primary 03E35, Secondary 03E45 |
| url | https://arxiv.org/abs/2504.04902 |