Journal of Symbolic Logic

The reducts of equality up to primitive positive interdefinability

Manuel Bodirsky, Hubie Chen, and Michael Pinsker

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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.

Article information

J. Symbolic Logic, Volume 75, Issue 4 (2010), 1249-1292.

First available in Project Euclid: 4 October 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C40: Interpolation, preservation, definability
Secondary: 08A40: Operations, polynomials, primal algebras 08A70: Applications of universal algebra in computer science 03D15: Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]

relational structure reduct primitive positive definition lattice invariant relation Galois connection local clone permutations


Bodirsky, Manuel; Chen, Hubie; Pinsker, Michael. The reducts of equality up to primitive positive interdefinability. J. Symbolic Logic 75 (2010), no. 4, 1249--1292. doi:10.2178/jsl/1286198146.

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