The expression is this:
$\bigcup_{n\in\mathbb{N}}\ \bigcup_{a_0\in\mathbb{Z}}\cdots\bigcup_{a_n\in\mathbb{Z}}\big\{z\in\mathbb{C}:a_0z^n+a_1z^{n-1}+\cdots+a_{n-1}z+a_n=0\big\}.$
I hope it's clear what this is meant to denote (the set of algebraic numbers), but I'm uneasy about it since the number of unions depends on an element in the first union.
I suspect that the set could be rewritten more concretely as a union indexed by $\mathbb{Z}$-valued sequences that eventually terminate, but I'm not sure how that would look.