The reducts of equality up to primitive positive interdefinability

Manuel Bodirsky; Hubie Chen; Michael Pinsker

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arXiv · 0810.2270

The reducts of equality up to primitive positive interdefinability

Manuel Bodirsky·Hubie Chen·Michael 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.

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Manuel Bodirsky, Hubie Chen, Michael Pinsker. 2010-01-16. The reducts of equality up to primitive positive interdefinability. https://arxiv.org/abs/0810.2270

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