Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-20T08:22:05.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Reducts of (C, +, ·) which contain +

Published online by Cambridge University Press:  12 March 2014

D. Marker  and
A. Pillay
D. Marker
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60680
A. Pillay
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the structure (C, +, ·) has no proper non locally modular reducts which contain +. In other words, if X ⊂ Cn is constructible and not definable in the module structure (C, +, λa)a Є C (where λa denotes multiplication by a) then multiplication is definable in (C, +, X).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 1243 - 1251
Copyright
Copyright © Association for Symbolic Logic 1990

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

[B2]Bouscaren, E., The group configuration—after E. Hrushovski, The model theory of groups (Nesin, A. and Pillay, A., editors), University of Notre Dame Press, Notre Dame, Indiana, 1989, pp. 199–209.Google Scholar
[C]Conway, J., Functions of one complex variable, 2nd ed., Springer-Verlag, Berlin, 1978.CrossRefGoogle Scholar
[H]Hrushovski, E., Contributions to stable model theory, Ph. D. thesis, University of California, Berkeley, California, 1986.Google Scholar
[HP]Hrushovski, E. and Pillay, A., Weakly normal groups, Logic Colloquium '85, North-Holland, Amsterdam, 1987, pp. 233–244.CrossRefGoogle Scholar
[M]Martin, G., Definability in reducts of algebraically closed fields, this Journal, vol. 53 (1988), pp. 188–199.Google Scholar
[P]Poizat, B., Groupes stables, Nur al-Mantiq wal-Ma'rifah, Villeurbanne, 1987.Google Scholar
[Z]Zilber, B., Some remarks on the model theory of algebraically closed fields, preprint, 1989.Google Scholar
[ZR]Zilber, B. and Rabinovitch, E., Additive reducts of algebraically closed fields, manuscript, 1988.Google Scholar