On a new proof completeness of p. i. Propositional Calculus


In this paper, in order to obtain some interesting properties of the implicational algebras, we prove a completeness theorem on positive implicational Propositional Calculus in which we use the axiom schema ((a \supset b) \supset b) \supset ((b \supset a) \supset a) in an essential manner. We demonstrate this theorem without using neither Zorn’s Lemma, nor similar properties.

DOI Code: 10.1285/i15900932v27n1p139

Keywords: Implication; Algebras

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