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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... (Update)
Context of citations to this paper: More
...in the Tarski reduct of a Qn algebra. In brief: MAn = S Rd T Q n : This theorem is in contrast to recent results obtained in [Hirsch Hodkinson 1997] stating that for every n 4, the variety MAn 1 is not finitely based over MAn . 2 Q algebras It is the aim of this section to...
.... attention to the way that games can be played on algebras can shed quite considerable light on the nature of the algebras [HH97a, HH98, HH97b, HH99, HM98] Would De Morgan would have been satisfied with games and the axioms they produce, as a contribution to understanding the...
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BibTeX entry: (Update)
R. Hirsch and I. Hodkinson, "Relation algebras with n-dimensional relational bases", manuscript, 1997. http://citeseer.ist.psu.edu/article/hirsch99relation.html More
@article{ hirsch00relation,
author = "Robin Hirsch and Ian M. Hodkinson",
title = "Relation Algebras with n-Dimensional Relational Bases",
journal = "Annals of Pure and Applied Logic",
volume = "101",
number = "2-3",
pages = "227-274",
year = "2000",
url = "citeseer.ist.psu.edu/article/hirsch99relation.html" }
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