NDLI: A Preliminary Study of MV-Algebras with Two Quantifiers Which Commute

Content Provider	Springer Nature Link
Author	Orella, Aldo Figallo
Copyright Year	2016
Abstract	In this paper we investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal-free two-dimensional cylindric algebras (see Henkin et al., in Cylindric algebras, 1985). In the 40s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two-dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia (Ann Pure Appl Logic 128(1-3):125–139, 2004) related to the characterization of a quantifier in terms of some special sub-algebra associated to it. On the other hand, we present a topological duality for this class of algebras and we apply it to characterize the congruences of one algebra via certain closed sets. Finally, we study the subvariety of this class generated by a chain of length n + 1 (n < ω). We prove that the subvariety is semisimple and we characterize their simple algebras. Using a special functional algebra, we determine all the simple finite algebras of this subvariety.
Starting Page	931
Ending Page	956
Page Count	26
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	104
Issue Number	5
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-02-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Monadic MV-algebras Diagonal-free two-dimensional cylindric algebras Simple algebras Subdirect products and subdirect irreducibility Model-theoretic forcing Cylindric and polyadic algebras; relation algebras Logic Mathematical Logic and Foundations Computational Linguistics
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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