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Transactions of the American Mathematical Society

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A sheaf-theoretic duality theory for cylindric algebras

Author: Stephen D. Comer
Journal: Trans. Amer. Math. Soc. 169 (1972), 75-87
MSC: Primary 02J15; Secondary 55B30
MathSciNet review: 0307908
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Abstract: Stone's duality between Boolean algebras and Boolean spaces is extended to a dual equivalence between the category of all $ \alpha $-dimensional cylindric algebras and a certain category of sheaves of such algebras. The dual spaces of important types of algebras are characterized and applications are given to the study of direct and subdirect decompositions of cylindric algebras.

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  • [2] William Hanf, On some fundamental problems concerning isomorphism of Boolean algebras, Math. Scand. 5 (1957), 205–217. MR 0108451
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Keywords: Cylindric algebras, sheaves, sectional representations, Boolean spaces, Stone representation theorem, dual space of a cylindric algebra
Article copyright: © Copyright 1972 American Mathematical Society