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partial algebras; varieties; weak subalgebras; weak equations
We study the weak hereditary class $S_{w}(\mathcal K)$ of all weak subalgebras of algebras in a total variety $\mathcal K$. We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.
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