Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
Duality theorems for finite structures (characterising gaps and good characterisations)
Journal of Combinatorial Theory Series B
A Characterisation of First-Order Constraint Satisfaction Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
Homomorphism preservation theorems
Journal of the ACM (JACM)
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We observe a number of connections between recent developments in the study of constraint satisfaction problems, irredundant axiomatisation and the study of topological quasivarieties. Several restricted forms of a conjecture of Clark, Davey, Jackson and Pitkethly are solved: for example we show that if, for a finite relational structure M, the class of M-colourable structures has no finite axiomatisation in first order logic, then there is no set (even infinite) of first order sentences characterising the continuously M-colourable structures amongst compact totally disconnected relational structures. We also refute a rather old conjecture of Gorbunov by presenting a finite structure with an infinite irredundant quasi-identity basis.