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The 116 reducts of (ℚ, <, a)

Published online by Cambridge University Press:  12 March 2014

Markus Junker  and
Martin Ziegler
Markus Junker
Affiliation:
Mathematisches Institut, Abteilung für Mathematische Logik, Universität Freiburg, Germany, E-mail: markus.junker@math.uni-freiburg.de
Martin Ziegler
Affiliation:
Mathematisches Institut, Abteilung für Mathematische Logik, Universität Freiburg, Germany, E-mail: ziegler@uni-freiburg.de
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 861 - 884
Copyright
Copyright © Association for Symbolic Logic 2008

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