The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice
L(
K) of all subquasivarieties for some quasivariety
K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.
Keywords Quasivariety -
Q-lattice - join-semidistributive -
Q-universality - independent basis - graph
Special issue of Studia Logica: 
Algebraic Theory of Quasivarieties
Presented by
Ryszard Wójcicki