Dimension of Generic Reals
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910047140839424 |
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| author | Miao, Yiping |
| author_facet | Miao, Yiping |
| contents | This paper investigates the Hausdorff measure of certain sets of generics in computability theory. Let $Γ$ be the Turing ideal in which we take the dense open sets. The set of $Γ$-Cohen generics has measure positive if and only if the gauge function is not dominated by every element in $Γ$, under some mild restrictions on the gauge function. The set of $Γ$-Mathias generics and the set of $Γ$-Sacks generics have measure positive if and only if the gauge function eventually dominates every element in $Γ$. This gives some comparison between the behavior of reals in the set and the measure of the set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension of Generic Reals Miao, Yiping Logic This paper investigates the Hausdorff measure of certain sets of generics in computability theory. Let $Γ$ be the Turing ideal in which we take the dense open sets. The set of $Γ$-Cohen generics has measure positive if and only if the gauge function is not dominated by every element in $Γ$, under some mild restrictions on the gauge function. The set of $Γ$-Mathias generics and the set of $Γ$-Sacks generics have measure positive if and only if the gauge function eventually dominates every element in $Γ$. This gives some comparison between the behavior of reals in the set and the measure of the set. |
| title | Dimension of Generic Reals |
| topic | Logic |
| url | https://arxiv.org/abs/2603.08952 |