New-from-old full dualities via axiomatisation

We study different full dualities based on the same finite algebra. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too. We use this theorem to obtain a better understanding of several important examples...

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Bibliographic Details
Published inAnnals of pure and applied logic Vol. 169; no. 7; pp. 588 - 615
Main Authors Davey, Brian A., Pitkethly, Jane G., Willard, Ross
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2018
Subjects
Alter ego
Full duality
Natural duality
Universal Horn axiomatisation
08C15
Alter ego
Universal Horn axiomatisation
08C20
Natural duality
Full duality
03C07
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Summary:We study different full dualities based on the same finite algebra. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too. We use this theorem to obtain a better understanding of several important examples from the theory of natural dualities. We also clarify what it means for two full dualities based on the same finite algebra to be different. Throughout the paper, a fundamental role is played by the universal Horn theory of the dual categories.
ISSN:0168-0072
DOI:10.1016/j.apal.2018.02.005