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Weak representations of relation algebras and relational bases

Published online by Cambridge University Press:  12 March 2014

Robin Hirsch ,
Ian Hodkinson  and
Roger D. Maddux
Robin Hirsch
Affiliation:
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK, E-mail: r.hirsch@ucl.ac.uk
Ian Hodkinson
Affiliation:
Department of Computing, Imperial College London, London SW7 2AZ, UK, E-mail: i.hodkinson@imperial.ac.uk
Roger D. Maddux
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA 50011, USA, E-mail: maddux@iastate.edu
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Abstract

It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RAn and wRRA contains the other.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 870 - 882
Copyright
Copyright © Association for Symbolic Logic 2011

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