Spencer Breiner: The logical spectrum and the logical structure sheaf

Mathematical logic seminar –  April 17, 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

Abstract:

In a pair of lectures (4/3, 4/17) 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.