The reducts of equality up to primitive positive interdefinability

Journal of Symbolic Logic 75 (4):1249-1292 (2010)
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 continum 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
Keywords relational structure   reduct   primitive positive definition   lattice   invariant relation   Galois connection   local clone   permutations
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DOI 10.2178/jsl/1286198146
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