Generalized deductive systems in subregular varieties

An algebra A = (A,F) is subregular alias regular with respect to a unary term function g if for each Θ, Φ ∈ Con A we have Θ = Φ whenever [g(a)]Θ = [g(a)]Φ for each a ∈ 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 ⊆ A is a class of some congruence on Θ containing g(a) if and only if C is this generalized deductive s…