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  1.  20
    Constraint Satisfaction, Irredundant Axiomatisability and Continuous Colouring.Marcel Jackson & Belinda Trotta - 2013 - Studia Logica 101 (1):65-94.
    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 (...)
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  2.  28
    Flat Algebras and the Translation of Universal Horn Logic to Equational Logic.Marcel Jackson - 2008 - Journal of Symbolic Logic 73 (1):90-128.
    We describe which subdirectly irreducible flat algebras arise in the variety generated by an arbitrary class of flat algebras with absorbing bottom element. This is used to give an elementary translation of the universal Horn logic of algebras, and more generally still, partial structures into the equational logic of conventional algebras. A number of examples and corollaries follow. For example, the problem of deciding which finite algebras of some fixed type have a finite basis for their quasi-identities is shown to (...)
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  3.  17
    Undecidability of Representability as Binary Relations.Robin Hirsch & Marcel Jackson - 2012 - Journal of Symbolic Logic 77 (4):1211-1244.
    In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.
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