A Tame Generic Structure with Non-Algebraic Geometric Closure
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866912647089225728 |
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| author | Jalili, Somaye Pourmahdian, Massoud Valizadeh, Ali N. |
| author_facet | Jalili, Somaye Pourmahdian, Massoud Valizadeh, Ali N. |
| contents | By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed generic structures in which the geometric closure is not included in the algebraic closure while the resulting theory is decidable. We show that paracollapsed structures have the strict order property and $\text{TP}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_04034 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Tame Generic Structure with Non-Algebraic Geometric Closure Jalili, Somaye Pourmahdian, Massoud Valizadeh, Ali N. Logic 03C45, 03C30, 03C10, 05C65 F.4.1 By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed generic structures in which the geometric closure is not included in the algebraic closure while the resulting theory is decidable. We show that paracollapsed structures have the strict order property and $\text{TP}_2$. |
| title | A Tame Generic Structure with Non-Algebraic Geometric Closure |
| topic | Logic 03C45, 03C30, 03C10, 05C65 F.4.1 |
| url | https://arxiv.org/abs/2011.04034 |