Fragments of the propositional calculus

Publisher Website
Google Scholar
Abstract
Of the several methods for proving the completeness of sets of axioms for the prepositional calculus perhaps the simplest is due to Kalmár, although it does not appear to be widely known. In this paper we generalize Kalmár's method to indicate how to obtain a complete axiomatization of any fragment of the propositional calculus which includes material implication. We shall carry through the description and proofs for the case where, in addition to a symbol for implication, there is just one other primitive truth-function symbol. For systems in which there are no other function symbols, or more than one other such symbol, notational changes but not conceptual changes will be required.

This publication has 1 reference indexed in Scilit: