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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

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