There is sometimes a sense in which one theory "posits less structure" than another theory. For example, it is standard to say that Galilean spacetime posits less structure than Newtonian spacetime since the former is obtained by "taking something away" - namely, the standard of absolute rest - from the latter. But it is unclear what this relationship might amount to in general. There are a number of proposals currently on the table for how to best compare the amounts of structure that different theories posit. Barrett's aim in this talk is to demonstrate how these proposals are related to one another, and to evaluate them on their own merits. In order to do so, he will present a collection of small results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ definability theorems. 

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