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

Marker, D.; Pillay, A.

Marker, D. ; Pillay, A.

J. Symbolic Logic, Tome 55 (1990) no. 1, p. 1243-1251 / Harvested from Project Euclid

Résumé

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 $(\mathbf{C},+,X)$.

Publié le : 1990-09-14
Classification:

@article{1183743417,
     author = {Marker, D. and Pillay, A.},
     title = {Reducts of $(C, +, \cdot)$ which Contain +},
     journal = {J. Symbolic Logic},
     volume = {55},
     number = {1},
     year = {1990},
     pages = { 1243-1251},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743417}
}

Marker, D.; Pillay, A. Reducts of $(C, +, \cdot)$ which Contain +. J. Symbolic Logic, Tome 55 (1990) no. 1, pp.  1243-1251. http://gdmltest.u-ga.fr/item/1183743417/