Dimension theory for the asymptotic couple of the field of logarithmic transseries
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918183074529280 |
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| author | Gehret, Allen Kaplan, Elliot Pynn-Coates, Nigel |
| author_facet | Gehret, Allen Kaplan, Elliot Pynn-Coates, Nigel |
| contents | In this paper we completely characterize all dimension functions on all models of the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries (Dimension Theorem). This is done by characterizing the "small" $1$-variable definable sets (Small Sets Theorem). As a byproduct, we show that $T_{\log}$ is d-minimal and does not eliminate imaginaries. Separately, we provide an abstract criterion for d-minimality, which we use to observe some new examples of d-minimal expansions of valued fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension theory for the asymptotic couple of the field of logarithmic transseries Gehret, Allen Kaplan, Elliot Pynn-Coates, Nigel Logic In this paper we completely characterize all dimension functions on all models of the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries (Dimension Theorem). This is done by characterizing the "small" $1$-variable definable sets (Small Sets Theorem). As a byproduct, we show that $T_{\log}$ is d-minimal and does not eliminate imaginaries. Separately, we provide an abstract criterion for d-minimality, which we use to observe some new examples of d-minimal expansions of valued fields. |
| title | Dimension theory for the asymptotic couple of the field of logarithmic transseries |
| topic | Logic |
| url | https://arxiv.org/abs/2507.01760 |