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Undecidability of representability as binary relations

Published online by Cambridge University Press:  12 March 2014

Robin Hirsch  and
Marcel Jackson
Robin Hirsch
Affiliation:
Department of Computer Science, University College London, London WC1E 6BT, UK, E-mail: [email protected]
Marcel Jackson
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia, E-mail: [email protected]
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Abstract

In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.

Keywords

Relation algebrabinary relationsrepresentabilityBoolean monoidlattice ordered monoidBrandt semigroup
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1211 - 1244
Copyright
Copyright © Association for Symbolic Logic 2012

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