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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.08247 |
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Table of Contents:
- We define $Ψ$-autoreducible sets given an autoreduction procedure $Ψ$. Then, we show that for any $Ψ$, a measurable class of $Ψ$-autoreducible sets has measure zero. Using this, we show that classes of cototal, uniformly introenumerable, introenumerable, and hyper-cototal enumeration degrees all have measure zero. By analyzing the arithmetical complexity of the classes of cototal sets and cototal enumeration degrees, we show that weakly 2-random sets cannot be cototal and weakly 3-random sets cannot be of cototal enumeration degree. Then, we see that this result is optimal by showing that there exists a 1-random cototal set and a 2-random set of cototal enumeration degree. For uniformly introenumerable degrees and introenumerable degrees, we utilize $Ψ$-autoreducibility again to show the optimal result that no weakly 3-random sets can have introenumerable enumeration degree. We also show that no 1-random set can be introenumerable.