Predicate and Set-Theoretic Calculi Based on Logic Without Contractions

In this paper the author studies the effect of eliminating the contraction rules from the Gentzen predicate calculus, and also from set-theoretic systems based on this calculus. It turns out that the predicate calculus without contraction rules is complete relative to finite models, and eliminating contraction rules from set-theoretic systems does not change the number of derivable formulas as long as the systems contain certain natural axioms. Bibliography: 4 titles.