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Duality Theory for Projective Algebras

  • Alasdair Urquhart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)

Abstract

Projective algebras were introduced by Everett and Ulam [4] 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 [2] 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 [11] has some interesting suggestions on the use of these algebras in the theory of parallel computation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alasdair Urquhart
    • 1
  1. 1.University of TorontoCanada

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