Pure Denumerable Lukasiewiczian Implication
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C. A. Meredith, to whom the above axioms are due, suggested in correspondence with McCall that Cl-C4 suffice for the C-pure fragment of the denumerably many-valued logic Lxo, also given by truth value stipulation with operators C and N in [2]. At the time, as we reported, we were unable to verify that claim (which, indeed, we had conjectured independently on the basis of Meredith's [3]). It turns out, however, that the method of [1] may be modified to verify Meredith's result. It was conjectured by Lukasiewicz and proved by Rose and Rosser in [4] that LX0 is axiomatized by C1-C42 together with modus ponens and
[1] C. A. Meredith. The dependence of an axiom of Łukasiewicz , 1958 .
[2] C. C. Chang. Proof of an axiom of Łukasiewicz , 1958 .
[3] A. R. Turquette,et al. Independent Axioms for Infinite-Valued Logic , 1963, Journal of Symbolic Logic.
[4] J. Rosser,et al. Fragments of many-valued statement calculi , 1958 .