Journal of Symbolic Logic

The reducts of equality up to primitive positive interdefinability

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

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

Digital Object Identifier
doi:10.2178/jsl/1286198146

Mathematical Reviews number (MathSciNet)
MR2767967

Zentralblatt MATH identifier
05835165

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.