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.
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Jackson, M., Trotta, B. Constraint Satisfaction, Irredundant Axiomatisability and Continuous Colouring. Stud Logica 101, 65–94 (2013). https://doi.org/10.1007/s11225-012-9372-4
- Irredundant axiomatisability
- Standard topological quasivarieties
- Graph dualities
- Constraint satisfaction problems