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Natural dualities for semilattice-based algebras

✍ Scribed by B. A. Davey; M. Jackson; J. G. Pitkethly; M. R. Talukder


Publisher
Springer
Year
2007
Tongue
English
Weight
449 KB
Volume
57
Category
Article
ISSN
0002-5240

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Natural Dualities for Varieties of MV-Al
✍ Philippe Niederkorn πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 133 KB

MV-algebras are the Lindenbaum algebras for Łukasiewicz's infinite-valued logic, just as Boolean algebras correspond to the classical propositional calculus. The finitely generated subvarieties of the variety M M of all MV-algebras are generated by finite chains. We develop a natural duality, in the

Functor category dualities for varieties
✍ B.A. Davey; M.R. Talukder πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 228 KB

Let A be a ΓΏnitely generated variety of Heyting algebras and let SI(A) be the class of subdirectly irreducible algebras in A. We prove that A is dually equivalent to a category of functors from SI(A) into the category of Boolean spaces. The main tool is the theory of multisorted natural dualities.