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The weak hereditary class of a variety

Wiktor BartolFrancesc Rosselló — 2006

Czechoslovak Mathematical Journal

We study the weak hereditary class S w ( 𝒦 ) of all weak subalgebras of algebras in a total variety 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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