Completeness for axiomatic extensions of modal logic with the master modality
Jan Rooduijn, Yde Venema

Abstract:
We apply the technique of filtration to prove completeness for a class of axiomatic extensions of modal logic with the master modality. It suffices that the set of additional axioms is basic modal, canonical and admits filtration. We also take some steps towards generalising our results to sets of extra axioms formulated in the full language.