Linear Reducts of the Complex Field

Notre Dame Journal of Formal Logic 45 (3):161-190 (2004)
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A reduct of a first-order structure is another structure on the same set with perhaps fewer definable predicates. We consider reducts of the complex field which are proper but nontrivial in a sense to be made precise in the paper. Our main result lists seven kinds of reducts. The list is complete in the sense that every reduct is a finite cover of one of these. We also investigate when two items on our list can be the same, in a couple of natural senses



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A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Weakly minimal groups of unbounded exponent.James Loveys - 1990 - Journal of Symbolic Logic 55 (3):928-937.
On locally modular, weakly minimal theories.James Loveys - 1993 - Archive for Mathematical Logic 32 (3):173-194.

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