Автори: A.P. Pynko

Анотація: Morgan-/Kleene-Stone (MS/) lattices are axiomatized by the constant-free identities of those axiomatizing Morgan-Stone (MS) algebras / «and the Kleene identity axiomatizing Kleene lattices relatively {De} Morgan ones». Such is said to be [quasi-strong|] «a [nearly] Morgan/Kleene lattice» iff every element of it [«exceeded by» exceeding its negation] exceeds its double negation, any Morgan/Kleene lattice being so. Applying the technique of characteristic functions of prime filters as homomorphisms from lattices onto the two-element chain one and their functional products, we prove that the variety of MS lattices is the quasi-variety enerated by a six-element one having an equational disjunctive system and expanding the direct product of the three- and two-element chain lattices, in which case subdirectly-irreducible MS lattices are exactly isomorphic copies of nine non-one-element pair-wise-non-isomorphic subalgebras of the six-element generating MS lattice, and so we get a 29-element non-chain distributive lattice of varieties of MS lattices subsuming the four-/three-element chain one of Morgan/Stone lattices/algebras (viz., constant-free versions of De Morgan algebras)/(more precisely, their term-wise definitionally equivalent constant-free versions, called Stone lattices). Among other things, we provide an REDPC scheme for MS lattices. Laying a special emphasis onto the universal/[quasi-]equational unbounded approximation of MS algebras (viz., the greatest iversal/[quasi]equational class of MS lattices without members with both bounds but expandable to no MS algebra) with members being exactly quasi-strong MS lattices, we find a 29/75-element non-chain distributive/nondistributive lattice of quasi-varieties of quasi-strong/nearly MS/Kleene lattices «subsuming the fifteen-element one of the [quasi-]equational join (viz., the [quasi-]variety generated by the union) of Morgan and Stone lattices, in its turn, subsuming the eight-element non-chain distributive one of those of the variety of Morgan lattices found earlier»/. On the other hand, that of nearly Morgan lattices is proved to have a countable decreasing chain with non-finitely-axiomatizable intersection.

ISBN 979-8326949523 (online).

Відповідальна установа: V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine

Видано: Kindle Direct Publishing,

Кількість сторінок: 134