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The number of modalities in T supplemented by the axiom CL2pL3p
Published online by Cambridge University Press: 12 March 2014
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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.
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- Copyright © Association for Symbolic Logic 1962