A sufficient condition for closed classes of $k$-valued logic to have only trivial congruences

V. V. Gorlov


Abstract: In this paper the author obtains a classification of $M$-classes of closed classes of $k$-valued logic that are minimal (with respect to inclusion) relative to the property “all superclasses have only trivial congruences”, and an algorithm for constructing $M$-classes is proposed. On the basis of a description of $M$-classes, a sufficient condition is obtained for triviality of congruences of closed classes of $k$-valued logic.
Bibliography: 11 titles.

UDC: 517.1

MSC: Primary 03G20, 03B50; Secondary 03F65, 08A30

Received: 16.02.1979

 English version: Mathematics of the USSR-Sbornik, 1981, 38:4, 507–532

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