Noncummulative cylindric algebras and relativizations of cylindric algebras

Bulletin of the Section of Logic 17 (2):75-81 (1988)
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Abstract

We obtain the class NA of noncommutative cylindric algebras from the class CA of cylindric algebras by weakening the axiom C4 of commutativity of cylindrifications . Some motivation for studying noncommutative cylindric algebras: Noncommutative cylindric algebras have the same “substitutional structure” as cylindric algebras , where substitutional structure refers to the equational behaviour of the substitution operations, the s i j ’s. For certain technical reasons, NA’s turn out to be useful in the study of the substitutional structure of CA’s. Cf. Thm. 3 below.

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The free non-commutative cylindric algebras are not atomic.Mohamed Khaled - 2017 - Logic Journal of the IGPL 25 (5):673-685.

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