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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1805.06767 |
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| _version_ | 1866915217953259520 |
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| author | Barbina, Silvia Casanovas, Enrique |
| author_facet | Barbina, Silvia Casanovas, Enrique |
| contents | A Steiner triple system is a set $S$ together with a collection $\mathcal{B}$ of subsets of $S$ of size 3 such that any two elements of $S$ belong to exactly one element of $\mathcal{B}$. It is well known that the class of finite Steiner triple systems has a Fra\"ıssé limit $M_{\mathrm{F}}$. Here we show that the theory $T^\ast_\mathrm{Sq}$ of $M_{\mathrm{F}}$ is the model completion of the theory of Steiner triple systems. We also prove that $T^\ast_\mathrm{Sq}$ is not small and it has quantifier elimination, $\mathrm{TP}_2$, $\mathrm{NSOP}_1$, elimination of hyperimaginaries and weak elimination of imaginaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_06767 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Model theory of Steiner triple systems Barbina, Silvia Casanovas, Enrique Logic A Steiner triple system is a set $S$ together with a collection $\mathcal{B}$ of subsets of $S$ of size 3 such that any two elements of $S$ belong to exactly one element of $\mathcal{B}$. It is well known that the class of finite Steiner triple systems has a Fra\"ıssé limit $M_{\mathrm{F}}$. Here we show that the theory $T^\ast_\mathrm{Sq}$ of $M_{\mathrm{F}}$ is the model completion of the theory of Steiner triple systems. We also prove that $T^\ast_\mathrm{Sq}$ is not small and it has quantifier elimination, $\mathrm{TP}_2$, $\mathrm{NSOP}_1$, elimination of hyperimaginaries and weak elimination of imaginaries. |
| title | Model theory of Steiner triple systems |
| topic | Logic |
| url | https://arxiv.org/abs/1805.06767 |