 Another challenge faced by the model-theoretic account is due to the limitations of its set-theoretic basis. Recall that models are sets. The worry is that truth-preservation over models might not guarantee necessary truth preservation—moreover, it might not even guarantee material truth preservation (truth preservation in the actual world). The reason is that each model domain is a set, but the actual world presumably contains all sets, and as a collection which includes all sets is too ‘‘large’’ to be a set (it constitutes a proper class), the actual world is not accounted for by any model (see Shapiro 1987).