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Krull dimension and elimination theory over the integers
Let $K:=\mathbb{C}$, and let $R:=K[x_1,\dots , x_n]$.
Then, a system of polynomial equations $p_1=0, p_2=0, \dots , p_r = 0$, where the $p_i$ are polynomials in the $x_j$, has finitely many solutions …