The number of modalities in T supplemented by the axiom CL2pL3p
Takeo Sugihara · Journal of Symbolic Logic · 1962
It is shown in Sobociński [1] that the number of irreducible modalities in T is infinite. The infinity of modalities in T collapses if the axiom CLpL2p is added to T, since T plus CLpL2p is equivalent to S4 and the number of irreducible modalities in S4 is finite as proved in Parry [2]. But the addition of the axiom CL2pL3p does not collapse the infinity of modalities in T. The aim of the present paper is to prove this theorem and its corollaries.