$\mathsf{MA} (\mathcal{I}$) and a Failure of Separation on the third Level
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915594337517568 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | We present a method which forces the failure of $Π^1_3$ and $Σ^1_3$-separation, while $\mathsf{MA} (\mathcal{I}$) holds, for $\mathcal{I}$ the family of indestructible ccc forcings. This shows that, in contrast to the assumption $\mathsf{BPFA}$ and $\aleph_1=\aleph_1^L$ which implies $Π^1_3$-separation, that weaker forcing axioms do not decide separation on the third projective level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathsf{MA} (\mathcal{I}$) and a Failure of Separation on the third Level Hoffelner, Stefan Logic We present a method which forces the failure of $Π^1_3$ and $Σ^1_3$-separation, while $\mathsf{MA} (\mathcal{I}$) holds, for $\mathcal{I}$ the family of indestructible ccc forcings. This shows that, in contrast to the assumption $\mathsf{BPFA}$ and $\aleph_1=\aleph_1^L$ which implies $Π^1_3$-separation, that weaker forcing axioms do not decide separation on the third projective level. |
| title | $\mathsf{MA} (\mathcal{I}$) and a Failure of Separation on the third Level |
| topic | Logic |
| url | https://arxiv.org/abs/2507.01187 |