Mathematical logic seminar – March 20 and April 3, 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
In a pair of lectures (3/20, 4/3) 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.
In the first lecture 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. The structure sheaf will be the subject of the second lecture.