finite algebras. For pseudovarieties, there is no general finitary counterpart to Birkhoff's theorem, but in many cases the introduction of a more complex notion of equations allows similar results to be derived. Pseudovarieties are of particular importance in the study of finite semigroups and hence in formal language theory. Eilenberg's theorem, often referred to as the variety theorem, describes a natural correspondence between varieties of regular languages and pseudovarieties of finite semigroups. See also Quasivariety Notes External links Two monographs available free online: Stanley N. Burris and H.P. Sankappanavar (1981), A Course in Universal Algebra. Springer-Verlag. . [Proof of Birkhoff's Theorem is in II§11.] Peter Jipsen and Henry Rose (1992), Varieties of Lattices, Lecture Notes in Mathematics 1533. Springer Verlag. . Universal algebra