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REDUCTS OF STRUCTURES AND MAXIMAL-CLOSED PERMUTATION GROUPS

Published online by Cambridge University Press:  14 September 2016

MANUEL BODIRSKY  and
DUGALD MACPHERSON
MANUEL BODIRSKY
Affiliation:
INSTITUT FÜR ALGEBRA TU DRESDEN 01062 DRESDEN GERMANY E-mail:Manuel.Bodirsky@tu-dresden.de
DUGALD MACPHERSON
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF LEEDS LEEDS LS2 9JT, UK E-mail: h.d.macpherson@leeds.ac.uk
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Abstract

Answering a question of Junker and Ziegler, we construct a countable first order structure which is not ω-categorical, but does not have any proper nontrivial reducts, in either of two senses (model-theoretic, and group-theoretic). We also construct a strongly minimal set which is not ω-categorical but has no proper nontrivial reducts in the model-theoretic sense.

Keywords

reductsmaximal closed subgroupsJordan permutation groupsD-relations

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 1087 - 1114
Copyright
Copyright © The Association for Symbolic Logic 2016 

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