Time:  12:00  13:20 
Room: 
Wean Hall 7201

Speaker: 
Spencer Breiner Department of Philosophy Carnegie Mellon University 
Title: 
The logical spectrum and the logical structure sheaf

Abstract: 
I will present a schemetype representation/duality theorem for logic and model theory. Grothendieck's theory of schemes in algebraic geometry begins with the representation of a ring R as a topological space (the spectrum) together with a structure sheaf, and R is recovered as the global sections of that sheaf. I will describe the `logical spectrum' for a theory, a topological groupoid built from models and isomorphisms of the theory. The syntax of the theory has a natural interpretation as certain `definable' sheaves on the space, and these are characterized by equivariance relative to isomorphisms. I will construct the structure sheaf of a theory from these definable sheaves. 