The domination monoid in o-minimal theories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866915195538898944 |
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| author | Mennuni, Rosario |
| author_facet | Mennuni, Rosario |
| contents | We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with arxiv:1702.06504, this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_01770 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The domination monoid in o-minimal theories Mennuni, Rosario Logic 03C45 (Primary) 03C64, 03C60, 12J10 (Secondary) We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with arxiv:1702.06504, this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields. |
| title | The domination monoid in o-minimal theories |
| topic | Logic 03C45 (Primary) 03C64, 03C60, 12J10 (Secondary) |
| url | https://arxiv.org/abs/2008.01770 |