Generic derivations, differential largeness, and NTP$_2$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910015947800576 |
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| author | Kaplan, Elliot Kesting, Christoph |
| author_facet | Kaplan, Elliot Kesting, Christoph |
| contents | We compare Fornasiero and Terzo's framework of generic derivations on algebraically bounded structures with León Sánchez and Tressl's differentially large fields. We show in the case of a single derivation that genericity and differential largeness coincide for éz-fields, as introduced by Walsberg and Ye. We also show that an NTP$_2$ algebraically bounded structure remains NTP$_2$ after expanding by a generic derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic derivations, differential largeness, and NTP$_2$ Kaplan, Elliot Kesting, Christoph Logic We compare Fornasiero and Terzo's framework of generic derivations on algebraically bounded structures with León Sánchez and Tressl's differentially large fields. We show in the case of a single derivation that genericity and differential largeness coincide for éz-fields, as introduced by Walsberg and Ye. We also show that an NTP$_2$ algebraically bounded structure remains NTP$_2$ after expanding by a generic derivation. |
| title | Generic derivations, differential largeness, and NTP$_2$ |
| topic | Logic |
| url | https://arxiv.org/abs/2508.13919 |