Trace definability II: model-theoretic linearity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917486784413696 |
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| author | Walsberg, Erik |
| author_facet | Walsberg, Erik |
| contents | We give examples of $\mathrm{NIP}$ structures in which new algebraic structure appears in the Shelah completion. In particular we construct a weakly o-minimal structure $\mathscr{M}$ such that $\mathscr{M}$ does not interpret an infinite group but the Shelah completion of $\mathscr{M}$ interprets an infinite field. We introduce a weak notion of interpretability called local trace definability between first order structures and an associated weak notion of equivalence. We give a dichotomy between ``linearity" and ``field structure" for dp-minimal expansions of archimedean ordered abelian groups. We also prove several other results about trace definability and local trace definability between various classes of structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12323 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Trace definability II: model-theoretic linearity Walsberg, Erik Logic We give examples of $\mathrm{NIP}$ structures in which new algebraic structure appears in the Shelah completion. In particular we construct a weakly o-minimal structure $\mathscr{M}$ such that $\mathscr{M}$ does not interpret an infinite group but the Shelah completion of $\mathscr{M}$ interprets an infinite field. We introduce a weak notion of interpretability called local trace definability between first order structures and an associated weak notion of equivalence. We give a dichotomy between ``linearity" and ``field structure" for dp-minimal expansions of archimedean ordered abelian groups. We also prove several other results about trace definability and local trace definability between various classes of structures. |
| title | Trace definability II: model-theoretic linearity |
| topic | Logic |
| url | https://arxiv.org/abs/2605.12323 |