Ian Hodkinson

The variety generated by completions of representable relation algebras

The variety V generated by the completions of representable relation algebras was defined in a recent paper of Maddux (Subcompletions of representable relation algebras, Algebra Universalis (2018) 79:20). Maddux noted that V is strictly larger than the class RRA of representable relation algebras. Andréka and Németi then showed that V is strictly contained in the class RA of relation algebras (and in fact there are continuum-many varieties between them), so answering Problem 1.1(1) of Maddux's paper. This might suggest that V is nearer to RRA than to RA. However, in the talk, I will sketch a proof that RRA is not finitely axiomatisable over V. The proof uses games and graphs.

Links:
https://arxiv.org/abs/1810.04569
https://link.springer.com/article/10.1007/s00012-018-0493-0