Journal of Symbolic Logic

Reducts of $(C, +, \cdot)$ which Contain +

D. Marker and A. Pillay

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Abstract

We show that the structure $(\mathbf{C},+,\cdot)$ has no proper non locally modular reducts which contain +. In other words, if $X \subset \mathbf{C}^n$ is constructible and not definable in the module structure $(\mathbf{C},+,\lambda_a)_{a \in \mathbf{C}}$ (where $\lambda_a$ denotes multiplication by $a$) then multiplication is definable in $(\mathbf{C},+,X)$.

Article information

Source
J. Symbolic Logic, Volume 55, Issue 3 (1990), 1243-1251.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743417

Mathematical Reviews number (MathSciNet)
MR1071326

Zentralblatt MATH identifier
0721.03023

JSTOR
links.jstor.org

Citation

Marker, D.; Pillay, A. Reducts of $(C, +, \cdot)$ which Contain +. J. Symbolic Logic 55 (1990), no. 3, 1243--1251. https://projecteuclid.org/euclid.jsl/1183743417


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