Journal of Symbolic Logic

The reducts of equality up to primitive positive interdefinability

Manuel Bodirsky, Hubie Chen, and Michael Pinsker

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

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

Dates
First available in Project Euclid: 4 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1286198146

Digital Object Identifier
doi:10.2178/jsl/1286198146

Mathematical Reviews number (MathSciNet)
MR2767967

Zentralblatt MATH identifier
05835165

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.jsl/1286198146.


Export citation