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 and false for all fields of characteristic greater than . We also prove that for each , there is a first-order formula that when interpreted in a finitely generated field is true for elements if and only if the elements are algebraically dependent over the prime field in
Citation
Bjorn Poonen. "Uniform first-order definitions in finitely generated fields." Duke Math. J. 138 (1) 1 - 21, 15 May 2007. https://doi.org/10.1215/S0012-7094-07-13811-0
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