Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T08:42:35.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Theories with equational forking

Published online by Cambridge University Press:  12 March 2014

Markus Junker  and
Ingo Kraus
Markus Junker
Affiliation:
Universität Freiburg, Institut für Mathematische Logik, Eckerstrasse 1, 79104 Freiburg, Germany, E-mail: junker@mathematik.uni-freiburg.de, URL: http://sunpool.mathematik.uni-freiburg.de/home/junker
Ingo Kraus
Affiliation:
Universität Freiburg, Institut für Mathematische Logik, Eckerstrasse 1, 79104 Freiburg, Germany, E-mail: kraus@logik.mathematik.uni-freiburg.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that equational independence in the sense of Srour equals local non-forking. We then examine so-called almost equational theories where equational independence is a symmetric relation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 326 - 340
Copyright
Copyright © Association for Symbolic Logic 2002

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]Buechler, S., Pillay, A., and Wagner, F., Elimination of hyperimaginaries for supersimple theories, Journal of the American Mathematical Society, vol. 14 (2001), no. 1, pp. 109–124.CrossRefGoogle Scholar
[2]Harnik, V. and Harrington, L., Fundamentals of forking, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 245–286.CrossRefGoogle Scholar
[3]Hrushovski, E., A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147–166.CrossRefGoogle Scholar
[4]Hrushovski, E. and Srour, G., On stable non-equational theories, manuscript.Google Scholar
[5]Junker, M., A note on equational theories, this Journal, vol. 65 (2000), no. 4, pp. 1705–1712.Google Scholar
[6]Junker, M. and Lascar, D., The indiscernible topology: A mock Zariski topology, Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 99–124.CrossRefGoogle Scholar
[7]Kim, B., Simple first order theories, Ph.D. thesis, University of Notre Dame, 1996.Google Scholar
[8]Kim, B., Simplicity, and stability in there, this Journal, vol. 66 (2001), no. 2, pp. 822–836.Google Scholar
[9]Kim, B. and Pillay, A., Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), no. 2-3, pp. 149–164.CrossRefGoogle Scholar
[10]Kraus, I., Lokale Stabilität in generischen Modellen, Ph.D. thesis, Universität Freiburg, 2001.Google Scholar
[11]Lascar, D., On the category of models of a complete theory, this Journal, vol. 47 (1984), no. 2, pp. 249–266.Google Scholar
[12]Lascar, D., Stabilité en théorie des modèles, 1986, Cabay, Louvain–la–Neuve.Google Scholar
[13]Pillay, A., Geometric Stability Theory, Clarendon Press, Oxford, 1996.CrossRefGoogle Scholar
[14]Pillay, A. and Poizat, B., Pas d'imaginaires dans l'infini!, this Journal, vol. 52 (1987), no. 2, pp. 400–403.Google Scholar
[15]Pillay, A. and Srour, G., Closed sets and chain conditions instable theories, this Journal, vol. 49 (1984), no. 4, pp. 1350–1362.Google Scholar
[16]Scheuermann, H., Generalized independence and canonical bases, in preparation.Google Scholar
[17]Scheuermann, H., Unabhängigkeitsrelationen, Diploma Thesis, Universität Freiburg, 1996.Google Scholar
[18]Srour, G., The independence relation in separably closedfields, this Journal, vol. 51 (1986), no. 3, pp. 715–725.Google Scholar