Diophantine Maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929557865496576 |
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| author | Eggink, A. |
| author_facet | Eggink, A. |
| contents | To prove that Hilbert's tenth problem over a ring R has a negative answer, usually the integers or another ring for which Hilbert's tenth problem has a negative solution is modelled inside the ring of interest. In this paper, we formalize this practice by introducing the notions of a Diophantine map and a Diophantine equivalence map. We compare the Diophantine case to the recursive case. We formalize a general version of Hilbert's tenth problem and show that we can transfer a positive or negative answer to Hilbert's tenth problem using effective Diophantine maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diophantine Maps Eggink, A. Logic Number Theory 03B25 (Primary) 11U05 (Secondary) To prove that Hilbert's tenth problem over a ring R has a negative answer, usually the integers or another ring for which Hilbert's tenth problem has a negative solution is modelled inside the ring of interest. In this paper, we formalize this practice by introducing the notions of a Diophantine map and a Diophantine equivalence map. We compare the Diophantine case to the recursive case. We formalize a general version of Hilbert's tenth problem and show that we can transfer a positive or negative answer to Hilbert's tenth problem using effective Diophantine maps. |
| title | Diophantine Maps |
| topic | Logic Number Theory 03B25 (Primary) 11U05 (Secondary) |
| url | https://arxiv.org/abs/2409.18845 |