Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-22T16:34:29.633Z Has data issue: false hasContentIssue false
  • English
  • Français

Directed free pseudospaces

Published online by Cambridge University Press:  12 March 2014

Romain Grunert
Romain Grunert*
Affiliation:
Freie Universität Berlin, Institut für Informatik, AG Theoretische Informatik, Takustraße 9, 14195 Berlin, Germany. E-mail: rgrunert@math.fu-berlin.de, Former affiliation: Humboldt-Universität zu Berlin, Institut für Mathematik E-mail: rgrunert@math.hu-berlin.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the free pseudospace is a reduct of a 1-based theory. This answers a question of David M. Evans. The theory is superstable, but not ω-stable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1176 - 1198
Copyright
Copyright © Association for Symbolic Logic 2010

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]Baldwin, John T., Fundamentals of stability theory, Perspectives in Mathematical Logic, Springer-Verlag, 1988.CrossRefGoogle Scholar
[2]Baudisch, Andreas and Pillay, Anand, A free pseudospace, this Journal, vol. 65 (2000), pp. 443–460.Google Scholar
[3]Evans, David M., Ample dividing, this Journal, vol. 68 (2003), pp. 1385–1402.Google Scholar
[4]Evans, David M., Trivial stable structures with non-trivial reducts, Journal of the London Mathematical Society. Second Series, vol. 72 (2005), pp. 351–363.CrossRefGoogle Scholar
[5]Evans, David M., Pillay, Anand, and Poizat, Bruno, A group in a group, Algebra and Logic, vol. 29 (1990), pp. 244–252.CrossRefGoogle Scholar
[6]Hrushovski, Ehud, A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147–166.CrossRefGoogle Scholar
[7]Hrushovski, Ehud and Pillay, Anand, Weakly normal groups, Logic Colloquium '85 (The Paris Logic Group, editor), Studies in Logic and the Foundations of Mathematics Volume 122, North-Holland, 1987, pp. 233–244.CrossRefGoogle Scholar
[8]Lachlan, Alistair H., Two conjectures regarding the stability of ω-categorical theories, Fundamenta Mathematicae, vol. 81 (1974), pp. 133–145.CrossRefGoogle Scholar
[9]Pillay, Anand, Stable theories, pseudoplanes and the number of countable models, Annals of Pure and Applied Logic, vol. 43 (1989), pp. 147–160.CrossRefGoogle Scholar
[10]Pillay, Anand, The geometry of forking and groups of finite Morley rank, this Journal, vol. 60 (1995), pp. 1251–1259.Google Scholar
[11]Pillay, Anand, Geometrie stability theory, Oxford Logic Guides 32, Clarendon Press, 1996.CrossRefGoogle Scholar
[12]Pillay, Anand, A note on CM-triviality and the geometry of forking, this Journal, vol. 65 (2000), pp. 474–480.Google Scholar
[13]Zil'ber, Boris I., Structural properties of models of ℵ1-categorical theories, Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of Science, Salzburg, 1983 (Marcus, Ruth Barcan, Dorn, Georg J. W., and Weingartner, Paul, editors), Studies in Logic and the Foundations of Mathematics, vol. 114, North-Holland, 1986, pp. 115–128.Google Scholar