← 研踪 PaperTrailarXiv:2611.08319 · v1
An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees (short version)
首次提交 2026-11-06 01:15
版本更新 2026-11-06 01:15
雷达观测 2026-11-06 12:09
摘要
The Arthur-Nimue-Merlin degrees are a generalization of the Turing degrees introduced by Kihara as a tangible description of the partially ordered set of Lawvere-Tierney topologies on the effective topos (equivalently, subtoposes of the effective topos). They are defined in terms of a three-player game that introduces both angelic and demonic non-determinism into oracle queries. We construct an order embedding of the Turing degrees with their order reversed into the Arthur-Nimue-Merlin degrees, whose image we call the "co-Turing degrees"; we then study the order relationship of these co-Turing degrees with the (naturally embedded) Turing degrees within the Arthur-Nimue-Merlin degrees. This is a short version of arXiv:2603.19946, focused on the main results.
作者备注：18 pages, comments welcome. Conference version of arXiv:2603.19946, accepted at CSL 2027
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v1 · 2026-11-06 01:15 · 最新观测版本
An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees (short version)
The Arthur-Nimue-Merlin degrees are a generalization of the Turing degrees introduced by Kihara as a tangible description of the partially ordered set of Lawvere-Tierney topologies on the effective topos (equivalently, subtoposes of the effective topos). They are defined in terms of a three-player game that introduces both angelic and demonic non-determinism into oracle queries. We construct an order embedding of the Turing degrees with their order reversed into the Arthur-Nimue-Merlin degrees, whose image we call the "co-Turing degrees"; we then study the order relationship of these co-Turing degrees with the (naturally embedded) Turing degrees within the Arthur-Nimue-Merlin degrees. This is a short version of arXiv:2603.19946, focused on the main results.
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