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arXiv · 2603.04067

The Construction Principle and superstability of free objects in varieties of algebras

Tapani Hyttinen·Gianluca Paolini·Davide Emilio Quadrellaro
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Abstract

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.

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Tapani Hyttinen, Gianluca Paolini, Davide Emilio Quadrellaro. 2026-03-04. The Construction Principle and superstability of free objects in varieties of algebras. https://arxiv.org/abs/2603.04067

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