Slupecki's fragmentary systems

Bulletin of the Section of Logic 13 (4):252-254 (1984)
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Abstract

In [1] J. S lupecki considers two fragmentary systems Sn and S ∗ n of the sentence calculus and gives the set of axioms for them. Let S be the set of all formulas constructed from propositional variables and the binary functor C. Recall that the set Sn consists of all formulas α having the property that the number of occurrences each variable in α is divisible by n. Sn is a system with respect of the rule of detachment and the rule of substitutions

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