Abstract
There is a well-known 1–1 correspondence between fully invariant—sometimes also called fully characteristic—congruences generated by sets of laws on the free anarchic universal algebra T of countable rank in a given finitary species τ and the varieties of algebras of species τ. This chapter presents the notion of a fully invariant algebraic closure system on the lattice Con T of congruences on T as a natural analogue of a fully invariant congruence on T such that a 1–1 correspondence arises between this kind of closure systems and quasi-varieties of algebras of species τ. The chapter also presents a theorem that states that a closure system H on a complete lattice L is called algebraic if H is an algebraic lattice with respect to the partial order ≦ of L.
Published Version
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