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Relative to any non-arithmetic set
Matthew Harrison-Trainor
https://arxiv.org/abs/2505.23613 https://arxiv.org/pdf/2505.23613

Relative to any non-arithmetic set
Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine which (upwards closed, Borel) classes of degrees form a degree spectrum. We resolve one of the major open problems in this area by showing that the non-arithmetic degrees are a degree spectrum. Our main new tool is a new form of unfriendly jump inversions wh…

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This https://arxiv.org/abs/2411.15293 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

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