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S-homogeneity and automorphism groups

Published online by Cambridge University Press:  12 March 2014

Elisabeth Bouscaren  and
Michael C. Laskowski
Elisabeth Bouscaren
Affiliation:
UFR de Mathematiques, Université de Paris VII, 75251 Paris Cedex 05, France, E-mail: [email protected]
Michael C. Laskowski
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, E-mail: [email protected]
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Abstract

We consider the question of when, given a subset A of M, the setwise stabilizer of the group of automorphisms induces a closed subgroup on Sym(A). We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that any subset of a countable, s-homogeneous, ω-stable structure induces a closed subgroup and contrast this with a number of negative results. We also show that for ω-stable structures s-homogeneity is preserved under naming countably many constants, but under slightly weaker conditions it can be lost by naming a single point.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1302 - 1322
Copyright
Copyright © Association for Symbolic Logic 1993

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