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Simple stable homogeneous groups

Published online by Cambridge University Press:  12 March 2014

Alexander Berenstein
Alexander Berenstein*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801-2975, USA, E-mail: [email protected]
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Abstract

We generalize tools and results from first order stable theories to groups inside a simple stable strongly homogeneous model.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1145 - 1162
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1] Yaacov, Itay Ben, Simplicity in compact abstract theories, Preprint, 2002.Google Scholar
[2] Yaacov, Itay Ben, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85–118.CrossRefGoogle Scholar
[3] Berenstein, Alexander and Buechler, Steven, Homogeneous expansions of Hilbert spaces, Preprint 2002.Google Scholar
[4] Buechler, Steven, Canonical bases in some supersimple theories, Preprint 1997.Google Scholar
[5] Buechler, Steven, Essential stability theory, Springer, 1996.CrossRefGoogle Scholar
[6] Buechler, Steven and Lessmann, Olivier, Simple Homogeneous models, Journal of the American Mathematical Society, vol. 16 (2003), no. 1, pp. 91–121.CrossRefGoogle Scholar
[7] Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), no. 1, pp. 293–309.Google Scholar
[8] Henson, Ward and Iovino, Jose, Ultraproducts in Analysis, Analysis and Logic, London Mathematical Society Lecture Note series, vol. 262 (2002).Google Scholar
[9] Hrushovski, Ehud, Unidimensional theories are superstable, Annals of Pure and Applied Logic, vol. 50 (1990), no. 2, pp. 117–138.CrossRefGoogle Scholar
[10] Hyttinen, Tapani and Lessmann, Olivier, Interpreting groups inside a strongly minimal homogeneous model, Preprint 2001.Google Scholar
[11] Kim, Byunghan and Pillay, Anand, Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), no. 2-3, pp. 149–164.CrossRefGoogle Scholar
[12] Lascar, Daniel, Omega stable groups, Model Theory and Algebraic Geometry, Lecture Notes in Mathematics, 1696, Springer, 1998.Google Scholar
[13] Marker, David, Introduction to the model theory of fields, Model theory of fields, Lecture Notes in Logic, 5, Springer, 1996.CrossRefGoogle Scholar
[14] Pillay, Anand, Geometric stability theory, Clarendon Press, 1996.CrossRefGoogle Scholar
[15] Pillay, Anand, Definability and definable groups in simple theories, this Journal, vol. 63 (1998), no. 3, pp. 788–796.Google Scholar
[16] Pillay, Anand, ω-stable groups, Model theory and algebraic geometry, Lecture Notes in Mathematics, 1696, Springer, 1998.Google Scholar
[17] Pillay, Anand, Forking in the category of existentially closed structures, Connections between model theory and algebraic and analytic geometry, Quaderni di Matematica, vol. 6, Aracne, Rome, 2000, pp. 23–42.Google Scholar
[18] Poizat, Bruno, Groupes stables, une tentative de conciliation entre la géometrie algébrique et la logique mathématique, Nur al-Mantiq wal-Marifah, Lyon, 1987.Google Scholar
[19] Shami, Ziv, Internality and type-definability of the automorphism group in simple theories, Preprint 2000.Google Scholar
[20] Shami, Ziv and Wagner, Frank, The binding group in simple theories, this Journal, vol. 67 (2002), no. 3, pp. 1016–1024.Google Scholar
[21] Wagner, Frank, Stable groups, Cambridge University Press, 1996.Google Scholar
[22] Wagner, Frank, Minimal fields, this Journal, vol. 65 (2000), no. 4, pp. 1833–1835.Google Scholar