Results for PHIL 251: Metalogic

In this course we will go through some of the seminal ideas, constructions, and results from modern logic, focusing especially on classical first-order ("predicate") logic. After introducing general ideas of induction and recursion, we will study a bit of elementary (axiomatic) set theory before then covering basic definability theory, viz. assessing the theoretical limits of what can and cannot be expressed in a first-order language. The centerpiece result of the class is the completeness - and closely related compactness - of first-order logic, a result with a number of momentous consequences, some useful, some philosophically puzzling. We will then study a connection with game theory, whereby a certain type of game characterizes precisely the expressive power of first-order logic. Further topics may include: the 0-1 law in finite model theory, second-order logic, and the algebraic approach to logic. Prerequisite: 150 or consent of instructor.