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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.13683 |
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| _version_ | 1866916009899720704 |
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| author | Gorman, Alexi Block Saban, Esther Elbaz |
| author_facet | Gorman, Alexi Block Saban, Esther Elbaz |
| contents | Given a structure $\mathcal{M}$ with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definable in $\mathcal{M}$. In response to questions raised by Dolich, Miller, and Steinhorn in their early work on open core, we prove that having an o-minimal open core is not an elementary property. In particular, we construct an expansion of the structure $(\mathbb{Q},<)$ that has an o-minimal open core, but some of its elementary superstructures do not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13683 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | O-minimal open core is not an elementary property Gorman, Alexi Block Saban, Esther Elbaz Logic 03C64 Given a structure $\mathcal{M}$ with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definable in $\mathcal{M}$. In response to questions raised by Dolich, Miller, and Steinhorn in their early work on open core, we prove that having an o-minimal open core is not an elementary property. In particular, we construct an expansion of the structure $(\mathbb{Q},<)$ that has an o-minimal open core, but some of its elementary superstructures do not. |
| title | O-minimal open core is not an elementary property |
| topic | Logic 03C64 |
| url | https://arxiv.org/abs/2605.13683 |