Primitive recursive categoricity spectra of functional structures
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908873135226880 |
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| author | Bazhenov, Nikolay Koh, Heer Tern Ng, Keng Meng |
| author_facet | Bazhenov, Nikolay Koh, Heer Tern Ng, Keng Meng |
| contents | For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non-$Δ_{1}^{0}$-categorical injection structures, and construct an example of a $Δ_{1}^{0}$-categorical injection structure for which these notions differ. Additionally, we also show that in every non-zero c.e.~Turing degree, there exists a PR-degree that is low for punctual isomorphism (to be defined), and also a PR-degree that is a degree of punctual categoricity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Primitive recursive categoricity spectra of functional structures Bazhenov, Nikolay Koh, Heer Tern Ng, Keng Meng Logic For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non-$Δ_{1}^{0}$-categorical injection structures, and construct an example of a $Δ_{1}^{0}$-categorical injection structure for which these notions differ. Additionally, we also show that in every non-zero c.e.~Turing degree, there exists a PR-degree that is low for punctual isomorphism (to be defined), and also a PR-degree that is a degree of punctual categoricity. |
| title | Primitive recursive categoricity spectra of functional structures |
| topic | Logic |
| url | https://arxiv.org/abs/2603.08010 |