In this paper, we concentrate on finite quasivarieties (i.e. classes of
finite algebras defined by quasi-identities). We present a motivation for studying finite quasivarieties. We introduce a new type of conditions that is well suited for defining finite quasivarieties and compare these new conditions with quasi-identities.
Keywords quasivariety - quasi-identity - pseudovariety - recursion - self-referential condition
Special issue of Studia Logica: 
Algebraic Theory of Quasivarieties
Presented by
M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko