Amalgamation and Interpolation in Abstract Algebraic Logic
Janusz Czelakowski, Don Pigozzi · 2003
algebraic logic provides a hierarchy of deductive systems based on how “algebra-like” their reduced semantics are. • S is protoalgebraic if Mod∗(S) is closed under subdirect products. • S is equivalential if Mod∗(S) is closed under submatrices and direct products. • S is finitely equivalential if Mod∗(S) is closed under submatrices, direct products, and ultraproducts. • S is algebraizable if it is equivalential and if A ∈Mod∗(S) then FA is the smallest S-filter of A. • S is finitely algebraizable if it is finitely equivalential and if A ∈Mod∗(S) then FA is the smallest S-filter of A.