The Consistency of the $\bf{Σ^1_3}$-Separation Property
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866918058135650304 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | We generically construct a model in which the $\bf{Σ^1_3}$-separation property is true, i.e. every pair of disjoint $\bf{Σ^1_3}$-sets can be separated by a $\bf{Δ^1_3}$-definable set. This answers an old question from the problem list $"$Surrealist landscape with figures$"$ by A. Mathias from 1968. We also construct a model in which the (lightface) $Σ^1_3$-separation property is true. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_11811 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Consistency of the $\bf{Σ^1_3}$-Separation Property Hoffelner, Stefan Logic 03E15, 03E35, 03E45 We generically construct a model in which the $\bf{Σ^1_3}$-separation property is true, i.e. every pair of disjoint $\bf{Σ^1_3}$-sets can be separated by a $\bf{Δ^1_3}$-definable set. This answers an old question from the problem list $"$Surrealist landscape with figures$"$ by A. Mathias from 1968. We also construct a model in which the (lightface) $Σ^1_3$-separation property is true. |
| title | The Consistency of the $\bf{Σ^1_3}$-Separation Property |
| topic | Logic 03E15, 03E35, 03E45 |
| url | https://arxiv.org/abs/1912.11811 |