= Schneider-Lang theorem
{c}
{title2=$|S|\le[K:\mathbb Q](\rho_1+\rho_2)$}
Let $f_1,\ldots,f_s$ be meromorphic functions with $f_j'\in K[f_1,\ldots,f_s]$ for a fixed <number field> $K$. Suppose $f_1,f_2$ are algebraically independent over $\mathbb C$ and have finite orders $\rho_1,\rho_2$. The set $S$ of points where every $f_j$ is finite and belongs to $K$ satisfies the displayed bound. The orders are growth orders for meromorphic functions. For $f_1=z$, $f_2=e^z$, the orders are zero and one and the functions are algebraically independent; an algebraic value of $e^\alpha$ at nonzero algebraic $\alpha$ would produce infinitely many such points $n\alpha$.
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