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THERE IS NO FINITE-VARIABLE EQUATIONAL AXIOMATIZATION OF REPRESENTABLE RELATION ALGEBRAS OVER WEAKLY REPRESENTABLE RELATION ALGEBRAS

Published online by Cambridge University Press:  12 August 2016

JEREMY F. ALM ,
ROBIN HIRSCH  and
ROGER D. MADDUX
JEREMY F. ALM*
Affiliation:
Department of Mathematics, Illinois College
ROBIN HIRSCH*
Affiliation:
Computer Science Department, University College London
ROGER D. MADDUX*
Affiliation:
Department of Mathematics, Iowa State University
*
*DEPARTMENT OF MATHEMATICS ILLINOIS COLLEGE JACKSONVILLE, IL 62650, USA E-mail: alm.academic@gmail.com
†COMPUTER SCIENCE DEPARTMENT UNIVERSITY COLLEGE LONDON GOWER STREET LONDON WC1E 6BT, UK E-mail: r.hirsch@ucl.ac.uk
‡DEPARTMENT OF MATHEMATICS IOWA STATE UNIVERSITY AMES, IA 50011, USA E-mail: maddux@iastate.edu
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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
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 3 , September 2016 , pp. 511 - 521
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

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