Model theory of Sheaves

Sam Dean

G.205,

Model theory is a branch of mathematics that deals with abstract algebraic structures, and properties of those which can be expressed in a "first order" way (that means, they can only be written down using finitely many ands, ors, nots, and quantifiers). Sheaves associate open sets in a topological space to an algebraic structure in such a way that consistent collections of elements can be "glued together" (like continuous functions). These gluing conditions are not first order statements - so you can't easily do the "model theory of sheaves" in the obvious way. However, I'm going to explain my recent work, which shows that one part of the model theory of modules, purity, can be extended to study purity of sheaves.

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