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Suppose I want to define a motivic integration over algebraically closed fields of positive characteristic (even countable), say $\bar{\mathbb{F}}_p$. Suppose that I additionally want the analogue of the change of variables formula that exists in the case of $\mathbb{C}$-varieties, and nothing more.

Precisely what prevents me from doing the usual construction in $\mathbb{C}$, and doing the usual proof of the change of variables that does not use resolution of singularities? How does model theory come into the picture?

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