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Small stable groups and generics

Published online by Cambridge University Press:  12 March 2014

Frank O. Wagner
Frank O. Wagner*
Affiliation:
Mathematical Institute, Oxford University, Oxford OX1 3LB, England Department of Mathematics and Statistics, McGill University, Montréal, Québec H3A 2K6, Canada
*
Mathematisches Institut, Universität Freiburg, Albertstr. 23b, W-7800 Freiburg, Germany
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Abstract

We define an ℜ-group to be a stable group with the property that a generic element (for any definable transitive group action) can only be algebraic over a generic. We then derive some corollaries for ℜ-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are ℜ-groups.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991 , pp. 1026 - 1037
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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