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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.03778 |
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Table of Contents:
- A Turing degree is d.c.e. if it contains a set that is the difference of two c.e. sets. A d.c.e. degree $\mathbf{d}$ is isolated if there exists a c.e. degree $\mathbf{a}<\mathbf{d}$ such that every c.e. degree below $\mathbf{d}$ is also below $\mathbf{a}$; $\mathbf{d}$ is upper isolated if there exists a c.e. degree $\mathbf{a}>\mathbf{d}$ such that every c.e. degree above $\mathbf{d}$ is also above $\mathbf{a}$; $\mathbf{d}$ is bi-isolated if it is both isolated and upper isolated. In this paper, we prove the existence of bi-isolated d.c.e. degrees in models of $\mathsf{I}Σ_1$.