Uniform first-order definitions in finitely generated fields
Number Theory
2017-04-03 v1 Logic
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 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.
Keywords
Cite
@article{arxiv.math/0507486,
title = {Uniform first-order definitions in finitely generated fields},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:math/0507486},
year = {2017}
}
Comments
14 pages