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Group configurations and germs in simple theories

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov*
Affiliation:
Équipe de Logique Mathématique, UFR de Mathématiques (Case 7012), Université Paris7, 2 Place Jussieu 75251 Paris Cedex 05, France, E-mail: [email protected] URL: http://www.logique.jussieu.fr/www.pezz

Abstract

We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an “almost” generic group chunk, where the product is defined up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Ben-Yaacov, Itay, Positive model theory and compact abstract theories, Preprint, 2002.CrossRefGoogle Scholar
[2]Ben-Yaacov, Itay, Thickness, and a categoric view of type-space functors, Preprint, 2002.CrossRefGoogle Scholar
[3]Ben-Yaacov, Itay, Tomašić, Ivan, and Wagner, Frank O., Constructing an almost-hyperdefinable group, Preprint, 2001.Google Scholar
[4]Ben-Yaacov, Itay and Wagner, Frank O., Almost orthogonality in simple theories, Preprint, 2001.Google Scholar
[5]Bouscaren, Elisabeth and Hrushovski, Ehud, On one-based theories, this Journal, vol. 59 (1994), no. 2. pp. 579595.Google Scholar
[6]Buechler, Steven, Pillay, Anand, and Wagner, Frank O., Supersimple theories, Journal of the American Mathematical Society, vol. 14 (2001), pp. 109124.CrossRefGoogle Scholar
[7]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293309.Google Scholar
[8]Kim, Byunghan, Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), no. 2, pp. 257267.CrossRefGoogle Scholar
[9]Kim, Byunghan, A note on lascar strong types in simple theories, this Journal, vol. 63 (1998), no. 3, pp. 926936.Google Scholar
[10]Kim, Byunghan and Pillay, Anand, Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 149164.CrossRefGoogle Scholar
[11]Pillay, Anand, Geometric stability theory, Clarendon Press, 1996.CrossRefGoogle Scholar
[12]Wagner, Frank O., Simple theories, Kluwer Academic Publishers, 2000.CrossRefGoogle Scholar
[13]Wagner, Frank O., Hyperdefinable groups in simple theories, Journal of Mathematical Logic, vol. 1 (2001), pp. 152172.CrossRefGoogle Scholar