With core c-representations we develop a new class of ranking models for conditional belief bases that combine the advantages of c-representations and System Z. On the one hand, they exhibit high-quality inferential behavior, just like c-representations, and on the other hand, they are stratified like the System Z ranking function, and can thus be constructed layer by layer. This allows for the identification of a unique minimal core c-representation from which we derive a new inductive inference operator, the c-core closure operator. This inference operator features conditional syntax splitting, like skeptical c-inference, and therefore does not suffer from the drowning problem, in contrast to System Z. Additionally, c-core closure satisfies rational monotony and inductive enforcement, and belongs to the class of basic defeasible entailment operators.
