The Construction Principle and superstability of free objects in varieties of algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917313961263104 |
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| author | Hyttinen, Tapani Paolini, Gianluca Quadrellaro, Davide Emilio |
| author_facet | Hyttinen, Tapani Paolini, Gianluca Quadrellaro, Davide Emilio |
| contents | We investigate the relationship between the Eklof-Mekler-Shelah Construction Principle for a variety of algebras $\mathbf{V}$ and the question of superstability of the free objects in $\mathbf{V}$, denoted as $\mathcal{F}_\mathbf{V}$. We consider this question in the general setting of AEC-coverings of $\mathcal{F}_\mathbf{V}$, with applications to first-order logic and beyond. Our main result is that if a strong form of the Construction Principle is satisfied, then almost all AEC-covering of $\mathcal{F}_\mathbf{V}$ are unsuperstable. Concrete applications to $R$-modules and varieties of groups are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Construction Principle and superstability of free objects in varieties of algebras Hyttinen, Tapani Paolini, Gianluca Quadrellaro, Davide Emilio Logic 08B20, 03C48, 03C05 We investigate the relationship between the Eklof-Mekler-Shelah Construction Principle for a variety of algebras $\mathbf{V}$ and the question of superstability of the free objects in $\mathbf{V}$, denoted as $\mathcal{F}_\mathbf{V}$. We consider this question in the general setting of AEC-coverings of $\mathcal{F}_\mathbf{V}$, with applications to first-order logic and beyond. Our main result is that if a strong form of the Construction Principle is satisfied, then almost all AEC-covering of $\mathcal{F}_\mathbf{V}$ are unsuperstable. Concrete applications to $R$-modules and varieties of groups are also considered. |
| title | The Construction Principle and superstability of free objects in varieties of algebras |
| topic | Logic 08B20, 03C48, 03C05 |
| url | https://arxiv.org/abs/2603.04067 |