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The forth part of the back and forth map in countable homogeneous structures

Published online by Cambridge University Press:  12 March 2014

S. J. McLeish
S. J. McLeish*
Affiliation:
Queen Mary and Westfield College, University of London, London, U.K., E-mail: sj.mcleish@ulst.ac.uk
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Abstract

The model theoretic ‘back and forth’ construction of isomorphisms and automorphisms is based on the proof by Cantor that the theory of dense linear orderings without endpoints is ℵ0-categorical. However, Cantor's method is slightly different and for many other structures it yields an injection which is not surjective. The purpose here is to examine Cantor's method (here called ‘going forth’) and to determine when it works and when it fails. Partial answers to this question are found, extending those earlier given by Cameron. We also give fuller characterisations of when forth suffices for model theoretic classes such as structures containing Jordan sets for the automorphism group, and ℵ0-categorical ω-stable structures. The work is based on the author's Ph.D. thesis.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 3 , September 1997 , pp. 873 - 890
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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