On the consistency of a three-valued logical calculus
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[This résumé was published in English in Matematicheskii Sbornik along with the article.]
The present paper contains an investigation of a three-valued logical calculus (the Σ system) previously described by the author [Recueil Mathématique 4 (46), 2 (1938)].
A constructive consistence proof is given for a part of this calculus rendering the results previously published concerning the Russell paradox. A method for a non-constructive completeness proof for the complete calculus is briefly indicated.
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