Universal-existential theories of fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911418866991104 |
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| author | Anscombe, Sylvy Fehm, Arno |
| author_facet | Anscombe, Sylvy Fehm, Arno |
| contents | We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines the universal-existential theories of the rational function field over k and of the field of Laurent series over k, and we find various many-one reductions between such fragments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal-existential theories of fields Anscombe, Sylvy Fehm, Arno Logic 03C60, 12L05, 12L12, 12J20, 14H05 We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines the universal-existential theories of the rational function field over k and of the field of Laurent series over k, and we find various many-one reductions between such fragments. |
| title | Universal-existential theories of fields |
| topic | Logic 03C60, 12L05, 12L12, 12J20, 14H05 |
| url | https://arxiv.org/abs/2405.12771 |