Uniform first-order definitions in finitely generated fields

Details Uniform first-order definitions in finitely generated fields Uniform first-order definitions in finitely generated fields

2005-07-22

arxiv.org/abs/math/0507486v1

Mathematics

Number Theory

14 pages

Scientific paper

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 >0. We also prove that for each n in N, there is a first-order formula psi_n(x_1,...,x_n) that when interpreted in a finitely generated field K is true for elements x_1,...,x_n in K if and only if the elements are algebraically dependent over the prime field in K.

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