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Preprint Number 19

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19. Markus Junker, Martin Ziegler
The 116 reducts of (Q,<,a)
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Submission date: 5 October 2006

Abstract:

This article is an attempt to classify the reducts of expansions of (Q,<) by unary predicates eliminating quantifiers (or equivalently to classify the closed subgroups of Sym(Q) containing the group of all automorphisms of (Q,<) fixing the predicates setwise), and to show that in each case there are only finitely many. This is completely achieved in the case of expansions by convex predicates, of which expansions by constants are a special case, and also in the case of a single dense, co-dense predicate. We have partial results in the general case of several dense predicates.

Mathematics Subject Classification: 03C, 20B27

Keywords and phrases : reducts, omega-categorical theories, automorphism groups

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