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The number of modalities in T supplemented by the axiom CL2pL3p

Published online by Cambridge University Press:  12 March 2014

Takeo Sugihara
Takeo Sugihara*
Affiliation:
Fukui University, Fukui, Japan
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Extract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 4 , December 1962 , pp. 407 - 408
Copyright
Copyright © Association for Symbolic Logic 1962

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References

[1] Bolesław Sobociński, Note on a modal system of Feys-von Wright, Journal of computing systems, Vol. 1 (1953), pp. 171–178.Google Scholar
[2] Parry, W. T., Modalities in the Survey system of strict implication, this Journal , Vol. 4 (1939), pp. 137–157.Google Scholar
[3] Prior, A. N., Time and Modality, Oxford, 1957, pp. 23–24.Google Scholar