## Relation Algebras with n-Dimensional Relational Bases (1999)

Venue: | Annals of Pure and Applied Logic |

Citations: | 9 - 2 self |

### BibTeX

@ARTICLE{Hirsch99relationalgebras,

author = {Robin Hirsch and Ian Hodkinson},

title = {Relation Algebras with n-Dimensional Relational Bases},

journal = {Annals of Pure and Applied Logic},

year = {1999},

volume = {101},

pages = {227--274}

}

### OpenURL

### Abstract

We study relation algebras with n-dimensional relational bases in the sense of Maddux. Fix n with 3 n !. Write Bn for the class of non-associative algebras with an n- dimensional relational basis, and RAn for the variety generated by Bn . We de ne a notion of representation for algebras in RAn , and use it to give an explicit (hence recursive) equational axiomatisation of RAn , and to reprove Maddux's result that RAn is canonical. We show that the algebras in Bn are precisely those that have a complete representation. Then we prove that whenever 4 n < l !, RA l is not nitely axiomatisable over RAn . This con rms a conjecture of Maddux. We also prove that Bn is elementary for n = 3; 4 only.