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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
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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

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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