Natural dualities for semilattice-based algebras
β 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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π SIMILAR VOLUMES
MV-algebras are the Lindenbaum algebras for Εukasiewicz'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
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.