## Cylindric Algebras, Part 1Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras. |

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algebra 21 algebra of dimension algebra of formulas algebraic structures analogous apply arbitrary assume BA's binary operation Boolean algebras CA's CAa's called cardinal characterization classes of algebras conclusion conditions are equivalent congruence relations consequence Corollary correlated cylindric algebras cylindric set algebra cylindrifications decomposition defined Definition denote direct products directly indecomposable discussion Don Pigozzi easily seen elementarily equivalent equation fact finite subset following conditions free algebras function fundamental operations given hence holds HSPK ideals implies induction infinite isomorphic isomorphism types K-freely language lattice lemma metalogical metamathematical non-discrete non-empty notion obtain obvious one-one ordinal particular polynomials predicate logic problem prove refinement property relational structures remarks following representable satisfying sentences sequence simple subalgebra subdirect subdirect product subreduct subuniverse symbols Tarski Theorem totally decomposable trivial ultrafilter ultraproducts variables weakly subdirectly indecomposable z-ideals zero-dimensional