MATHEMATICA BOHEMICA, Vol. 128, No. 3, pp. 319-324 (2003)
Generalized deductive systems in subregular varieties  Ivan
Chajda   Abstract: An algebra $\A= (A,F)$ is subregular alias
regular with respect to a unary term function $g$ if for each
$\Theta, \Phi\in\CA$ we have $\Theta= \Phi$ whenever
$[g(a)]_{\Theta} = [g(a)]_{\Phi}$ for each $a\in A$. We borrow
the concept of a deductive system from logic to modify it for
subregular algebras. Using it we show that a subset $C\subseteq
A$ is a class of some congruence on $\Theta$ containing $g(a)$
if and only if $C$ is this generalized deductive system. This
method is efficient (needs a finite number of steps).  Keywords:
regular variety, subregular variety, deductive system,
congruence class, difference system  Classification (MSC2000):
08A30, 08B05, 03B22  Full text of the article: