The variety MV of all MV-algebras is shown to be non-canonical in a strong sense. Specifically it is shown that the canonical extension of the Chang algebra, K 2 , is not an MV-algebra. As a consequence, no non-finitely generated variety of MV-algebras is canonical.
A backtracking algorithm with element order selection is presented, and its eeciency discussed in relation both to standard examples and to examples concerning relation-preserving maps which the algorithm was derived to solve.
A b s t r a c t. The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes. The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean… (More)
The context for this paper is a class of distributive lattice expansions, called double quasioperator algebras (DQAs). The distinctive feature of these algebras is that their operations preserve or reverse both join and meet in each coordinate. Algebras of this type provide algebraic semantics for certain non-classical propositional logics. In particular,… (More)
This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a 2-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in… (More)
Partition-induced natural dl alit& for varieties of pseudo-compicmented distrrbutivc lattices, Discrete Malhematics 113 (1993) 41-58. A natural dl:sitty is obtained for each finitely generated variety B,, (n < CG) of distributive p-algebras. 7 he duality for B,, is based on a schizophrenic object: E:, in B,, is the algebra 2 " @ 1 which gencrates the… (More)