4 papers
The homomorphism lattice induced by a finite algebra
Brian A. Davey, Charles T. Gray, Jane G. Pitkethly
Each finite algebra induces a lattice~ via the quasi-order~ on the finite members of the variety generated by~, where $\mathbf B…
New-from-old full dualities via axiomatisation
Brian A. Davey, Jane G. Pitkethly, Ross Willard
We clarify what it means for two full dualities based on the same algebra to be different. Our main theorem gives conditions on two different alter egos of a finite algebra under w…
Counting relations on Ockham algebras
Brian A. Davey, Long T. Nguyen, Jane G. Pitkethly
We find all finite Ockham algebras that admit only finitely many compatible relations (modulo a natural equivalence). Up to isomorphism and symmetry, these Ockham algebras form two…
Dualizability of automatic algebras
Wolfram Bentz, Brian A. Davey, Jane G. Pitkethly +1
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizab…