(Written June 24, 2026. Last updated June 24, 2026.) Rough prerequisite: I think this will make the most sense to you if you’ve seen multivariable calculus before, but all you really need to …

Recall from model theory that two structures are called elementarily equivalent if they satisfy the same first-order sentences. In other words, two structures $\frak A$ and $\frak B$ of the languag...