On the number of variables in the axioms.
M. D. Gladstone · Notre Dame Journal of Formal Logic · 1970
Introduction.There are three principal results.(1) A new proof is given of a theorem already obtained by Wajsberg (see [7]), and by Diamond and McKinsey (see [l]), to the effect that if a propositional calculus is complete then at least one of its axioms must contain >3 distinct variables.(For precise definitions of propositίonal calculus, complete, etc., see §2.) (2) The incomplete calculus whose axioms consist of all tautologies having 3, it is necessary and sufficient that every logical connective of the system has B)\-B.For the purposes of this paper,