, Volume 3, Issue 1, pp 3-12

On the consistency of a three-valued logical calculus

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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 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.