Uniform first-order definitions in finitely generated fields
Poonen, Bjorn
Duke Math. J., Tome 136 (2007) no. 1, p. 1-21 / Harvested from Project Euclid
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We prove that there is a first-order sentence in the language of rings that is true for all finitely generated fields of characteristic $0$ and false for all fields of characteristic greater than $0$ . We also prove that for each $n \in {\mathbb N}$ , there is a first-order formula $\psi_n(x_1,\ldots,x_n)$ that when interpreted in a finitely generated field $K$ is true for elements $x_1,\ldots,x_n \in K$ if and only if the elements are algebraically dependent over the prime field in $K$
Publié le : 2007-05-15
Classification:  11U09,  14G25 
@article{1178738559,
     author = {Poonen, Bjorn},
     title = {Uniform first-order definitions in finitely generated fields},
     journal = {Duke Math. J.},
     volume = {136},
     number = {1},
     year = {2007},
     pages = { 1-21},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178738559}
}

Poonen, Bjorn. Uniform first-order definitions in finitely generated fields. Duke Math. J., Tome 136 (2007) no. 1, pp.  1-21. http://gdmltest.u-ga.fr/item/1178738559/