The 116 reducts of (ℚ, <,a)

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

Reducts of the generic digraph.Lovkush Agarwal - 2016 - Annals of Pure and Applied Logic 167 (3):370-391.
Reducts of the Henson graphs with a constant.András Pongrácz - 2017 - Annals of Pure and Applied Logic 168 (7):1472-1489.
Reducts of the Random Bipartite Graph.Yun Lu - 2013 - Notre Dame Journal of Formal Logic 54 (1):33-46.

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References found in this work

Reducts of random hypergraphs.Simon Thomas - 1996 - Annals of Pure and Applied Logic 80 (2):165-193.

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