 to S3 we obtain a distinct system with 26 modalities also intermediate between S3 and S4. Therefore the number of modalities does not uniquely determine a system. Systems S1 and S2, as well as T and B, have an infinite number of modalities (Burgess 2009, chapter 3 on Modal Logic, discusses the additional systems S4.2 and S4.3 and explains well the reduction of modalities in different systems).