Equivalential fragment of the infinite valued logic of Lukasiewicz and the intermediate logics

Bulletin of the Section of Logic 9 (4):170-174 (1980)
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Abstract

It is obvious that the equivalential fragment of the innite-valued logic of Lukasiewicz is contained in the equivalential fragment of the clas- sical propositional logic. From the results of Kanzinski [2] it is follows that L$ 1 is also contained in the equivalential fragment of the intermediate logic LC3 determined by the pseudo-Boolean algebra of the three-element chain. In this paper we shall prove the following

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