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Transactions of the American Mathematical Society

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Cylindric algebras and algebras of substitutions


Author: Charles Pinter
Journal: Trans. Amer. Math. Soc. 175 (1973), 167-179
MSC: Primary 02J15
DOI: https://doi.org/10.1090/S0002-9947-1973-0317931-1
MathSciNet review: 0317931
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Abstract: Several new formulations of the notion of cylindric algebra are presented. The class $ C{A_\alpha }$ of all cylindric algebras of degree $ \alpha $ is shown to be definitionally equivalent to a class of algebras in which only substitutions (together with the Boolean $ + , \cdot $, and $ - $) are taken to be primitive operations. Then $ C{A_\alpha }$ is shown to be definitionally equivalent to an equational class of algebras in which only substitutions and their conjugates (together with $ + , \cdot $, and $ - $) are taken to be primitive operations.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0317931-1
Keywords: Cylindric algebra, cylindrification, diagonal element, algebraic logic
Article copyright: © Copyright 1973 American Mathematical Society

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