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September 2008 The 116 reducts of (ℚ, <,a)
Markus Junker, Martin Ziegler
J. Symbolic Logic 73(3): 861-884 (September 2008). DOI: 10.2178/jsl/1230396752

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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Markus Junker. Martin Ziegler. "The 116 reducts of (ℚ, <,a)." J. Symbolic Logic 73 (3) 861 - 884, September 2008. https://doi.org/10.2178/jsl/1230396752

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1189.03041
MathSciNet: MR2444273
Digital Object Identifier: 10.2178/jsl/1230396752

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 3 • September 2008
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