Journal of Symbolic Logic 73 (3):861-884 (2008)

Abstract
This article aims to classify those reducts of expansions of (Q, <) by unary predicates which eliminate quantifiers, and in particular to show that, up to interdefinability, there are only finitely many for a given language. Equivalently, we wish to classify the closed subgroups of Sym(Q) containing the group of all automorphisms of (Q, <) fixing setwise certain subsets. This goal is achieved for expansions by convex predicates, yielding expansions by constants as a special case, and for the expansion by a dense, co-dense predicate. Partial results are obtained in the general setting of several dense predicates
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DOI 10.2178/jsl/1230396752
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Reducts of Random Hypergraphs.Simon Thomas - 1996 - Annals of Pure and Applied Logic 80 (2):165-193.

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