Calculi of Pure Strict Implication

In July 1956 the following problem was proposed by D. Meredith: To axiomatise a propositional calculus with strict implication as the sole undefined functor. Using ‘C1–5’ for those portions of Lewis’s S1–5 which are expressible in terms of strict implication alone, this problem was solved for C5 in August 1956 by C. A. Meredith, who proved the adequacy of the single axiom CCCCCttpqCrsCCspCuCrp, with substitution and detachment (Sections IX-XI below). A variety of connected results were obtained by the authors on the way to this one. In what follows, we shall generally indicate who is chiefly responsible for which results; but it may be noted now that results relating to systems weaker than C5 (which will be mentioned from time to time in different sections) and also references to other items in the literature, are mainly due to Lemmon.