Embedding the prime model of real exponentiation into o-minimal exponential fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917610996629504 |
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| author | Krapp, Lothar Sebastian |
| author_facet | Krapp, Lothar Sebastian |
| contents | Motivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o-minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embeddable into any o-minimal exponential field, where the embedding is not necessarily elementary. This is a consequence of an unconditional model theoretic embeddability result that we obtain by applying Kőnig's Lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Embedding the prime model of real exponentiation into o-minimal exponential fields Krapp, Lothar Sebastian Logic 03C64 (03C60 12J15 12L12) Motivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o-minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embeddable into any o-minimal exponential field, where the embedding is not necessarily elementary. This is a consequence of an unconditional model theoretic embeddability result that we obtain by applying Kőnig's Lemma. |
| title | Embedding the prime model of real exponentiation into o-minimal exponential fields |
| topic | Logic 03C64 (03C60 12J15 12L12) |
| url | https://arxiv.org/abs/2302.01609 |