Congruence relations on de Morgan algebras

Various classes of de Morgan algebras whose congruence relations satisfy special conditions are investigated together with their interrelationship. In particular, the classes of congruence permutable, congruence regular, and congruence uniform de Morgan algebras are studied.Presented by Joel Berman.     

Subdirectly irreducible algebras with hyperidentities of the variety of De Morgan algebras

The paper characterizes the class of subdirectly irreducible algebras satisfying hyperidentities of the variety of De Morgan algebras. Such algebras are called subdirectly irreducible De Morgan quasilattices. The suggested characterization is quite close to that of the classical case of subdirectly irreducible DeMorgan algebras.     

Relatively pseudocomplemented Hilbert algebras

We characterise those Hilbert algebras that are relatively pseudocomplemented posets.      

Algebras with hyperidentities of the variety of De Morgan algebras

The paper characterizes the algebras with hyperidentities of the variety of De Morgan algebras. For these algebras with two binary operations we prove a structure theorem. As a consequence, we obtain a finite base of the hyperidentities for the variety of De Morgan algebras having functional and objective ranks not exceeding three.     

伪补分配格的同余理想与同余关系

L是完备的伪补分配格,I是L的同余理想,本文得到以下结果：⑴θ是L的以I为核的最大同余关系的条件。⑵L的以I为核的同余关系是唯一的充分必要条件。⑶L的同余理想与同余关系之间有一一对应关系的充分必要条件。     

The De Morgan Medal

The Ramanujan Journal -     

De Morgan classifying toposes

We present a general method for deciding whether a Grothendieck topos satisfies De Morgan's law (resp. the law of excluded middle) or not; applications to the theory of classifying toposes follow. Specifically, we obtain a syntactic characterization of the class of geometric theories whose classifying toposes satisfy De Morgan's law (resp. are Boolean), as well as model-theoretic criteria for theories whose classifying toposes arise as localizations of a given presheaf topos.