Some Results Concerning Axioms for Equivalential Calculus

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One of the most important questions in the area of the equivalential calculus (EC) currently is the issue of the single shortest axiom. We show some new a single organic and inorganic axioms for EC which are either D-complete or R-complete. We also present a number of two-element sets of axioms which posses some special properties. Two matrix are also discussed, which exclude two formulas from the set of potential 2MP-complete axioms.