Ultrapower ($M^I/\mathcal{U}$)

An ultrapower is an ultraproduct whose factors are all one structure $M$. Its elements are equivalence classes $[f]$ of functions $f:I\to M$, where $f\sim g$ exactly when $\{i\in I:f(i)=g(i)\}$ belongs to the chosen ultrafilter $\mathcal{U}$.