Let
K\mathcal{K}
be a finite collection of finite algebras of finite signature such that
SP(
K\mathcal{K}
) has meet semi-distributive congruence lattices. We prove that there exists a finite collection
K\mathcal{K}
1 of finite algebras of the same signature,
K1 Ê K\mathcal{K}_1 \supseteq \mathcal{K}
, such that
SP(
K\mathcal{K}
1) is finitely axiomatizable.We show also that if
HS(K) Í SP(K)HS(\mathcal{K}) \subseteq SP(\mathcal{K})
, then
SP(
K\mathcal{K}
1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.
Keywords quasivarieties - finite axiomatizability - pseudo-complemented congruence lattices - Willard terms
While working on this paper, the first author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant no. T37877 and the second author was supported by the US National Science Foundation grant no. DMS-0245622.
Special issue of Studia Logica: 
Algebraic Theory of Quasivarieties
Presented by
M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko