## Journal of Symbolic Logic

### S-Homogeneity and Automorphism Groups

#### 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 $\mathrm{Sym}(A)$. 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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744377

Mathematical Reviews number (MathSciNet)
MR1253924

Zentralblatt MATH identifier
0792.03018

JSTOR