Unreachability of Inductive-Like Pointclasses in $L(\mathbb{R})$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914365859430400 |
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| author | Levinson, Derek Neeman, Itay Sargsyan, Grigor |
| author_facet | Levinson, Derek Neeman, Itay Sargsyan, Grigor |
| contents | Hjorth proved from $ZF + AD + DC$ that there is no sequence of distinct $Σ^1_2$ sets of length $δ^1_2$. Sargsyan extended Hjorth's technique to show there is no sequence of distinct $Σ^1_{2n}$ sets of length $δ^1_{2n}$. Sargsyan conjectured an analogous property is true for any regular Suslin pointclass in $L(R)$ -- i.e. if $κ$ is a regular Suslin cardinal in $L(R)$, then there is no sequence of distinct $κ$-Suslin sets of length $κ^+$ in $L(R)$. We prove this in the case that the pointclass $S(κ)$ is inductive-like. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10076 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Unreachability of Inductive-Like Pointclasses in $L(\mathbb{R})$ Levinson, Derek Neeman, Itay Sargsyan, Grigor Logic 03E45 03E60 Hjorth proved from $ZF + AD + DC$ that there is no sequence of distinct $Σ^1_2$ sets of length $δ^1_2$. Sargsyan extended Hjorth's technique to show there is no sequence of distinct $Σ^1_{2n}$ sets of length $δ^1_{2n}$. Sargsyan conjectured an analogous property is true for any regular Suslin pointclass in $L(R)$ -- i.e. if $κ$ is a regular Suslin cardinal in $L(R)$, then there is no sequence of distinct $κ$-Suslin sets of length $κ^+$ in $L(R)$. We prove this in the case that the pointclass $S(κ)$ is inductive-like. |
| title | Unreachability of Inductive-Like Pointclasses in $L(\mathbb{R})$ |
| topic | Logic 03E45 03E60 |
| url | https://arxiv.org/abs/2210.10076 |