  Preferential semantics relies on a function S taking a set K of models into a subset S(K) of K. The crucial definition of preferential entailment stipulates that A is a (nonmonotonic) consequence of Γ if every model M of S(Models(Γ)) implies A. Shoham’s theory is based on a partial order ≼ over models: S(K) can then be characterized as the set of models in K that are ≼-minimal in K. To ensure that no set can preferentially entail a contradiction unless it classically entails a contradiction, infinite descending ≼ chains need to be disallowed.