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Constraint Satisfaction, Irredundant Axiomatisability and Continuous Colouring

Abstract

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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Correspondence to Marcel Jackson.

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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

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Keywords

  • Quasivariety
  • Antivariety
  • Irredundant axiomatisability
  • Standard topological quasivarieties
  • Graph dualities
  • Constraint satisfaction problems