The Ax-Kochen-Ershov principles via the higher valued hyperfield
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912250194821120 |
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| author | Lee, Junguk |
| author_facet | Lee, Junguk |
| contents | In this paper, we concern the model theory of finitely ramified henselian valued fields via higher valued hyperfields. Most of all, we provide a number of Ax-Kochen-Ershov Theorems for finitely ramified henselian valued fields relative to higher valued hyperfields. As corollaries, we deduce a transfer of decidability for full theories and existential theories of a finitely ramified henselian valued fields relative to higher valued hyperfields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Ax-Kochen-Ershov principles via the higher valued hyperfield Lee, Junguk Logic 03C60, 12L12 In this paper, we concern the model theory of finitely ramified henselian valued fields via higher valued hyperfields. Most of all, we provide a number of Ax-Kochen-Ershov Theorems for finitely ramified henselian valued fields relative to higher valued hyperfields. As corollaries, we deduce a transfer of decidability for full theories and existential theories of a finitely ramified henselian valued fields relative to higher valued hyperfields. |
| title | The Ax-Kochen-Ershov principles via the higher valued hyperfield |
| topic | Logic 03C60, 12L12 |
| url | https://arxiv.org/abs/2502.19863 |