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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1610.03331 |
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| _version_ | 1866908612657414144 |
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| author | Schrittesser, David |
| author_facet | Schrittesser, David |
| contents | Let $\mathcal R$ be a $Σ^1_1$ binary relation and call a set $\mathcal R$-discrete iff no two distinct of its elements are $\mathcal R$-related. We show that in the extension of $\mathbf{L}$ by iterated Sacks forcing, there is a $Δ^1_2$ maximal $\mathcal R$-discrete set, and thus the existence of such sets is compatible with the negation of the continuum hypothesis. As an application we find a $Π^1_1$ maximal orthogonal family of Borel probability measures in said extension. The basis of this is a new Ramsey theoretic result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_03331 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Definable discrete sets with large continuum Schrittesser, David Logic 03E15, 03E35 Let $\mathcal R$ be a $Σ^1_1$ binary relation and call a set $\mathcal R$-discrete iff no two distinct of its elements are $\mathcal R$-related. We show that in the extension of $\mathbf{L}$ by iterated Sacks forcing, there is a $Δ^1_2$ maximal $\mathcal R$-discrete set, and thus the existence of such sets is compatible with the negation of the continuum hypothesis. As an application we find a $Π^1_1$ maximal orthogonal family of Borel probability measures in said extension. The basis of this is a new Ramsey theoretic result. |
| title | Definable discrete sets with large continuum |
| topic | Logic 03E15, 03E35 |
| url | https://arxiv.org/abs/1610.03331 |