Uniform first-order definitions in finitely generated fields
Bjorn Poonen
Abstract
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 psin(x1,...,xn) that when interpreted in a finitely generated field K is true for elements x1,...,xn in K if and only if the elements are algebraically dependent over the prime field in K.
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