Duality Theory for Projective Algebras
Projective algebras were introduced by Everett and Ulam  as an algebraic formulation of the operations of projection and product on a two-dimensional algebra of relations. Although they were among the first structures to be investigated in the modern revival of the algebraic logic tradition, they have been somewhat overshadowed by their close kin, cylindric algebras and relation algebras. Chin and Tarski  showed that they can be viewed as two-dimensional cylindric algebras with special properties. Nevertheless, projective algebras are attractive as a natural axiomatic version of projection and product, and have a charm of their own. Ulam and Bednarek’s report of 1977  has some interesting suggestions on the use of these algebras in the theory of parallel computation.
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