| Abstract: | 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  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. |
