Theorie der Konsequenzoperationen und Grundbegriffe der Logik

We give an elementary introduction into the theory of consequence operations. We proof some elementary results concerning basic notions of logic like tautology, consistency, independence and completeness. We show in particular that every finite axiomatizable set is independent axiomatizable and that every consistent set has relative to a finitary consequence operation a maximal consistent extension. Finally we provide an abstract semantics for consequence operations