Symmetric operators on modal pseudocomplemented De Morgan algebras

Abstract

This paper aims at discussing the importance of Leibniz Law to getting models for Paraconsistent Set Theories.

A note on k-cyclic modal pseudocomplemented De Morgan algebras

“…Sometimes we write "tx" instead of "t(x)". It is worth mentioning that the class C k -algebra is a variety; and, as examples, we have the classes 1-cyclic mpM -algebra and 2-cyclic mpM -algebra were studied in [15] and [12], respectively. Now, we give a result to be used to characterize the prime spectrum for a given C kalgebra.…”

“…So, it is clear that the variety of C k -algebras is finitely generated and locally finite. Now, if we take k = 2, we obtain the simple algebras of the variety S-algebras studied in [12,Theorem 5.14]. Indeed:…”

“…Theorem 2.11 [12] Let A be an S-algebra. then, A is subdirectly irreducible if and only if A is isomorphic to a subalgebra of either T 2 4 or T 2 3 .…”

“…It is worth mentioning that the class of mpM −algebras constitutes a proper subvariety of the variety V 0 studied by H. Sankappanavar in [23]. More recently, the theory of operators over mpM −algebras was considered by Figallo-Orellano et al in [10,11,12]. In particular, they studied the class of mpM −algebras enriched with an automorphism of period 2 and k, where k is an positive integer; in fact, this automorphism works as a new unary operator.…”

“…In this paper, we will determine the condition to construct epimorphisms between finite symmetric mpM -algebras, with the purpose of computing them. To know how the epimorphisms can be built, it is useful, for instance, to determine the lattice of subvarieties of the variety of symmetric mpM -algebras, see [12,Section 7]. Furthermore, the construction of epimorphisms between two finite algebra can be used to compute the cardinality of free algebras in finite generated varieties as it was the case of [12,Section 6].…”