This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...

[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)].

In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...) result necessitates- the introduction of the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity—which the authors have chosen to call elementary propositions. The most general statements are formed by merely combining these variables by means of the two primitive propositional functions of propositions Negation and Disjunction; and the entire theory is concerned with the process of asserting those combinations which it regards as true propositions, employing for this purpose a few general rules which tell how to assert new combinations from old, and a certain number of primitive assertions from which to begin. (shrink)

In [1] D. A. Bochvar formulated a 3-valued logic. He analyzed the paradoxes of Russel and Weyl, and by means of the logic he proved that the paradox formulae were meaningless. In this paper the class of algebras corresponding to n- valued generalizations of the Bochovar's 3-valued logic is investigated. The class is dened axiomatically. The axiomatization for Bochovar's n-valued logic Bn is obtained on the basis of algebraic axiomatization.