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The reducts of equality up to primitive positive interdefinability

Published online by Cambridge University Press:  12 March 2014

Manuel Bodirsky ,
Hubie Chen  and
Michael Pinsker
Manuel Bodirsky
Affiliation:
Laboratoire d'Informatique (LIX), CNRS UMR 7161, École Polytechnique, 91128 Palaiseau, France. E-mail: [email protected], URL: http://www.lix.polytechnique.fr/~bodirsky/
Hubie Chen
Affiliation:
Departament de Tecnologies de la Informació i Les Comunicacions, Universität Pompeu Fabra, Barcelona, Spain. E-mail: [email protected], URL: http://www.tecn.upf.es/~hchen/
Michael Pinsker
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen, 14032 Caen Cedex, France. E-mail: [email protected], URL: http://dmg.tuwien.ac.at/pinsker/
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Abstract

We initiate the study of reducts of relational structures up to primitive positive interdefinability: After providing the tools for such a study, we apply these tools in order to obtain a classification of the reducts of the logic of equality. It turns out that there exists a continuum of such reducts. Equivalently, expressed in the language of universal algebra, we classify those locally closed clones over a countable domain which contain all permutations of the domain.

Keywords

relational structurereductprimitive positive definitionlatticeinvariant relationGalois connectionlocal clonepermutations
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1249 - 1292
Copyright
Copyright © Association for Symbolic Logic 2010

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