Mathematical logic seminar - April 3, April 17, May 1 2012

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


I will present a scheme-type 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.