A note on the non-existence of prime models of theories of pseudo-finite fields
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913975139041280 |
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| author | Chatzidakis, Zoé |
| author_facet | Chatzidakis, Zoé |
| contents | We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to κ-prime models, for κa regular uncountable cardinal or \aleph_ε. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_05593 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A note on the non-existence of prime models of theories of pseudo-finite fields Chatzidakis, Zoé Logic 03C50, 03C60, 12L12, Secondary 12E20 We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to κ-prime models, for κa regular uncountable cardinal or \aleph_ε. |
| title | A note on the non-existence of prime models of theories of pseudo-finite fields |
| topic | Logic 03C50, 03C60, 12L12, Secondary 12E20 |
| url | https://arxiv.org/abs/2004.05593 |