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NONREPRESENTABLE RELATION ALGEBRAS FROM GROUPS

Published online by Cambridge University Press:  13 June 2019

HAJNAL ANDRÉKA ,
ISTVÁN NÉMETI  and
STEVEN GIVANT
HAJNAL ANDRÉKA*
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
ISTVÁN NÉMETI*
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
STEVEN GIVANT*
Affiliation:
Department of Mathematics and Computer Science, Mills College
*
*ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES BUDAPEST, REÁLTANODA ST. 13-15, H-1053, HUNGARY E-mail: andreka.hajnal@renyi.mta.hu
†ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES BUDAPEST, REÁLTANODA ST. 13-15, H-1053, HUNGARY E-mail: nemeti.istvan@renyi.mta.hu
‡DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE MILLS COLLEGE 500 MACARTHUR BOULEVARD OAKLAND, CA 94613 USA E-mail: wang@mills.edu
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Abstract

A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We present our main construction in terms of polygroupoids.

Keywords

Primary 03G1520Bxx03GxxSecondary 03E2003C05grouprelation algebraBrandt groupoidpolygroupoidatom structurecomplex algebragroup relation algebranonrepresentable relation algebracoset algebrameasurable relation algebra
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 861 - 881
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Copyright
Copyright © Association for Symbolic Logic 2019 

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References

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