Syntactic foundations for unawareness of theorems

We provide a syntactic model of unawareness. By introducing multiple knowledge modalities, one for each sub-language, we specifically model agents whose only mistake in reasoning (other than their unawareness) is to underestimate the knowledge of more aware agents. We show that the model is a complete and sound axiomatization of the set-theoretic model of Galanis (University of Southampton Discussion paper 709, 2007) and compare it with other unawareness models in the literature.