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Coordinatisation by binding groups and unidimensionality in simple theories

Published online by Cambridge University Press:  12 March 2014

Ziv Shami
Ziv Shami*
Affiliation:
Department of Mathematics, University of Illinoisat Urbana Champaign, USA, E-mail: [email protected]
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Abstract.

In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence (ai \ i ≤ n*) ⊆ dcleq(a) with an* = a such that for every i ≤ n* if pi = tp(ai/{aj |j < i}) then Aut(pi / Q) is type-definable with its action on . A unidimensional simple theory eliminates the quantifier ∃∞ and either interprets (in Ceq) an infinite type-definable group or has the property that ACL(Q) = C for every infinite definable set Q.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004 , pp. 1221 - 1242
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

[BPW]Buechler, S., Pillay, A., and Wagner, F., Supersimple theories, Journal of the American Mathematical Society, vol. 14 (2001), pp. 109–124.Google Scholar
[HKP]Hart, B., Kim, B., and Pillay, A., Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293–309.Google Scholar
[HS]Hart, B. and Shami, Z., On the type-definability of the binding group in simple theories, this Journal, to appear.Google Scholar
[H]Hrushovski, E., Unidimensional theories are superstable, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 117–138.CrossRefGoogle Scholar
[HI]Hrushovski, E., Computing the Galois group of a linear differential equation (Appendix B), Differential galois theory, Banach Center Publications, vol. 58, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2002, pp. 97–138.Google Scholar
[K1]Kim, B., Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), pp. 257–267.CrossRefGoogle Scholar
[KP]Kim, B. and Pillay, A., Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 149–164.CrossRefGoogle Scholar
[Ne]Newelski, L., The diameter of a Lascar strong type, preprint.Google Scholar
[SI]Shami, Z., Internality and interpretable automorphism groups in simple theories, Annals of Pure and Applied Logic, vol. 129 (2004), no. 1–3, pp. 149–162.CrossRefGoogle Scholar
[SW]Shami, Z. and Wagner, F., On the binding group in simple theories, this Journal, vol. 67 (2002), no. 3, pp. 1016–1024.Google Scholar
[Sh-S]Shelah, S., Simple unstable theories, Annals of Mathematical Logic, vol. 19 (1980), pp. 177–203.CrossRefGoogle Scholar
[W]Wagner, Frank O., Simple theories, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.CrossRefGoogle Scholar
[W1]Wagner, Frank O., On almost orthogonality in simple theories, preprint.Google Scholar
[Z]Zilber, B., The structure of models of uncountably categorical theories, Proceedings of the international congress of mathematicians, vol. 1, 2 (Warsaw, 1983), PWN, Warsaw, 1984, pp. 359–368.Google Scholar