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Recovering the hyperdefinable group action in the group configuration theorem

Published online by Cambridge University Press:  12 March 2014

Byunghan Kim
Byunghan Kim*
Affiliation:
Yonsei University, Department of Mathematics, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, South Korea, E-mail: bkim@yonsei.ac.kr
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Abstract

In this paper, we continue the construction done in [3], so that under model-4-CA or 4-CA, given a bounded quadrangle C induced from a group configuration, we build a canonical hyperdefinable homogeneous space equivalent to C. When C is principal, we can choose the homogeneous space principal as well.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 12 - 24
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1] Kim, B. and Pillay, A., From stability to simplicity, The Bulletin of Symbolic Logic, vol. 4 (1998), pp. 17–36.CrossRefGoogle Scholar
[2] Pillay, A., Geometric Stability Theory, Oxford University Press, Oxford, 1996.CrossRefGoogle Scholar
[3] de Piro, T., Kim, B., and Millar, J., Constructing the hyperdefinable group from the group configuration, Journal of Mathematical Logic, vol. 6 (2006), pp. 121–139.Google Scholar
[4] Tomasic, I. and Wagner, F. O., Applications of the group configuration theorem in simple theories, Journal of Mathematical Logic, vol. 3 (2003), pp. 239–255.Google Scholar
[5] Wagner, F. O., Simple Theories, Kluwer Academic Publishers, Dordrecht, 2000.CrossRefGoogle Scholar