quasivariety

A class of L-algebras is a quasivariety if and only if it is closed under subalgebras, direct products and ultraproducts.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

F of A, the generalized matrix is a full model and AlgL is a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L and Eq is finite, then the quasivariety generated by

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

A quasivariety of L-algebras is a class of algebras which is the class of the models of some set of

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

The researchers in AAL are somehow surprised by the fact that several finitary and finitely algebraizable logics have a variety as its equivalent algebraic semantics, when the theory of algebraizable logics allows us in general to prove only that the equivalent algebraic semantics of a finitary and finitely algebraizable logic is a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

In fact this class of algebras is first-order definable but is not a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Since equations are quasiequations, each variety is a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Conversely, if a quasivariety is an Eq-algebraic semantics for a finitary

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

Alg*L is not only an SP-class, but a quasivariety and it is the quasivariety generated by any class of algebras K which is an equivalent semantics for

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006

L) but Alg*L is not this class ” in fact it is not even a quasivariety.

Propositional Consequence Relations and Algebraic Logic Jansana, Ramon 2006