Journal of Symbolic Logic

S-Homogeneity and Automorphism Groups

Elisabeth Bouscaren and Michael C. Laskowski

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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 $\mathrm{Sym}(A)$. We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that any subset of a countable, s-homogeneous, $\omega$-stable structure induces a closed subgroup and contrast this with a number of negative results. We also show that for $\omega$-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.

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J. Symbolic Logic, Volume 58, Issue 4 (1993), 1302-1322.

First available in Project Euclid: 6 July 2007

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Bouscaren, Elisabeth; Laskowski, Michael C. S-Homogeneity and Automorphism Groups. J. Symbolic Logic 58 (1993), no. 4, 1302--1322.

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