Visualization of the hyperreal numbers

Course Description:  An introduction to the basic concepts, methods, and results of metalogic. Logic is an ancient discipline that was traditionally concerned with the question of how to prove a statement. Metalogic is the modern incarnation of this discipline that takes provability itself—its scope, limits, and connections to other notions—as an object of study. The primary goal of this course is to understand the relationship between the notions of proof and interpretation. Our central theorem is Gödel’s completeness theorem, which says that a statement is provable if and only if there is no interpretation of the symbols appearing in the statement according to which it is false. Building on this and related results, we will develop techniques for constructing a wealth of unexpected, non-standard interpretations of axiomatic systems.

Syllabus TBA

Class Time and Location: T/R 11am - 12:15pm; 194 Mercer St, Room 304

Office Hours: TBA; 5 Washington Place, Room 308