Cofinitary groups and projective well-orders
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918012391522304 |
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| author | Fischer, Vera Schembecker, Lukas Schrittesser, David |
| author_facet | Fischer, Vera Schembecker, Lukas Schrittesser, David |
| contents | We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks, Miller, Miller partition forcing and Shelah's poset for diagonalizing maximal ideal. Introducing a new robust coding technique, we establish the relative consistency of $\mathfrak{a}_g=\mathfrak{d}<\mathfrak{c}=\aleph_2$ alongside the existence of a $Δ^1_3$-wellorder of the reals and a co-analytic witness for $\mathfrak{a}_g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16618 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cofinitary groups and projective well-orders Fischer, Vera Schembecker, Lukas Schrittesser, David Logic We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks, Miller, Miller partition forcing and Shelah's poset for diagonalizing maximal ideal. Introducing a new robust coding technique, we establish the relative consistency of $\mathfrak{a}_g=\mathfrak{d}<\mathfrak{c}=\aleph_2$ alongside the existence of a $Δ^1_3$-wellorder of the reals and a co-analytic witness for $\mathfrak{a}_g$. |
| title | Cofinitary groups and projective well-orders |
| topic | Logic |
| url | https://arxiv.org/abs/2312.16618 |