PHL 391 • Topics in Logic
7:00 PM-10:00 PM
This course studies advanced issues in the metatheory of first-order logic. We will begin with characterizations of the notions of recursive and recursively enumerable sets, and use these notions in proving the undecidability of first-order consequence, the undefinability of arithmetic truth, and the incompleteness of Peano arithmetic. We will then look in detail at this incompleteness result and Godel's second incompleteness theorem, considering alternative methods of proof and examining the robustness of the results under small variations in the logic. From there, we will work toward Lindstrom's characterization of first-order logic, working through the notions of finite and partial isomorphism and proving Fraisse's Theorem. Time permitting, we will investigate related topics in model theory, beginning with the Omitting Types Theorem and atomic and omega-saturated models (including Vaught's Theorem) and proceeding to the use of elementary chains in model construction.