Undecidability of the degree structure of primitive recursive m -reducibility
Let $\mathbf{C}^{pr}_{m}$ be the upper semilattice of degrees of computable sets with respect to primitive recursive $m$-reducibility. We prove that the first-order theory of $\mathbf{C}^{pr}_{m}$ is hereditarily undecidable.
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| Veröffentlicht in: | Journal of logic and computation 2024-11 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let $\mathbf{C}^{pr}_{m}$ be the upper semilattice of degrees of computable sets with respect to primitive recursive $m$-reducibility. We prove that the first-order theory of $\mathbf{C}^{pr}_{m}$ is hereditarily undecidable. |
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| ISSN: | 0955-792X 1465-363X |
| DOI: | 10.1093/logcom/exae074 |