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algebra universalis

, Volume 33, Issue 4, pp 516–532 | Cite as

The equational theory of union-free algebras of relations

  • H. Andréka
  • D. A. Bredikhin
Article

Abstract

We solve a problem of Jónsson [12] by showing that the class ℛ of (isomorphs of) algebras of binary relations, under the operations of relative product, conversion, and intersection, and with the identity element as a distinguished constant, is not axiomatizable by a set of equations. We also show that the set of equations valid in ℛ is decidable, and in fact the set of equations true in the class of all positive algebras of relations is decidable.

Keywords

Binary Relation Identity Element Relative Product Equational Theory Distinguished Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • H. Andréka
    • 1
  • D. A. Bredikhin
    • 2
  1. 1.Mathematical InstituteBudapestHungary
  2. 2.SaratovRussia

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