On the $Π^1_2$ consequences of $Π^1_1$-$\mathsf{CA}_0$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915030354624512 |
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| author | Suzuki, Yudai Yokoyama, Keita |
| author_facet | Suzuki, Yudai Yokoyama, Keita |
| contents | In this paper, we introduce a hierarchy dividing the set $\{σ\in Π^1_2 : Π^1_1$-$\mathsf{CA}_0 \vdash σ\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to $Π^1_1$-$\mathsf{CA}_0$: leftmost path principle, Ramsey's theorem for $Σ^0_n$ classes of $[\mathbb{N}]^{\mathbb{N}}$ and determinacy for $(Σ^0_1)_n$ classes of $\mathbb{N}^{\mathbb{N}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07136 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $Π^1_2$ consequences of $Π^1_1$-$\mathsf{CA}_0$ Suzuki, Yudai Yokoyama, Keita Logic In this paper, we introduce a hierarchy dividing the set $\{σ\in Π^1_2 : Π^1_1$-$\mathsf{CA}_0 \vdash σ\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to $Π^1_1$-$\mathsf{CA}_0$: leftmost path principle, Ramsey's theorem for $Σ^0_n$ classes of $[\mathbb{N}]^{\mathbb{N}}$ and determinacy for $(Σ^0_1)_n$ classes of $\mathbb{N}^{\mathbb{N}}$. |
| title | On the $Π^1_2$ consequences of $Π^1_1$-$\mathsf{CA}_0$ |
| topic | Logic |
| url | https://arxiv.org/abs/2402.07136 |