Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 75, Issue 4 (2010), 1249-1292.
The reducts of equality up to primitive positive interdefinability
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.
J. Symbolic Logic, Volume 75, Issue 4 (2010), 1249-1292.
First available in Project Euclid: 4 October 2010
Permanent link to this document
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]
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