 To encompass the whole class of logic systems one finds in the literature, a slightly more general definition than Tarski’s is required. We will say that an abstract consequence operation \(C\) on an arbitrary set \(A\) is an operation that applied to subsets of \(A\) gives subsets of \(A\) and for all \(X, Y \subseteq A\) satisfies the conditions (1), (2) and (4) above. If in addition \(C\) satisfies (3) we say that it is a finitary consequence operation.