With the very strong caveat that I know very little about logic and set theory, I will try to explain some ideas from logic which are relevant to some recent developments in motivic cohomology and algebraic geometry. One of the major technical obstacle in modern algebraic geometry is the failure of resolution of singularities in characteristic p > 0. Yet, from a certain viewpoint, this is purely a problem about valuation rings and ultraproducts thereof. I will explain how this was crucial in the construction of motivic cohomology in joint work with Matthew Morrow. Time permitting, I will dream about some other ways to use this principle, using condensed mathematics.