Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T11:14:43.470Z Has data issue: false hasContentIssue false
  • English
  • Français

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: aberenst@math.uiuc.edu
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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