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There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras

Alm, JF; Hirsch, R; Maddux, RD; (2016) There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras. The Review of Symbolic Logic , 9 (3) pp. 511-521. 10.1017/S1755020316000265. Green open access

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Abstract

We prove that any equational basis that defines representable relation algebras (RRA) over weakly representable relation algebras (wRRA) must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose small subalgebras are representable.

Type: Article
Title: There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S1755020316000265
Publisher version: http://dx.doi.org/10.1017/S1755020316000265
Language: English
Additional information: This article has been published in a revised form in The Review of Symbolic Logic http://dx.doi.org/10.1017/S1755020316000265. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2016 Association for Symbolic Logic.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1508668
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