The course extends the students' familiarity with the basic notions of logic to the meta-logic of the propositional calculus and of first order logic. The topics covers include a set theoretic characterization of formal languages and formal systems of logic, induction and recursion and a rigorous presentation of the basics of model theoretic semantics, proof of the compactness theorem for propositional logic and of soundness and completeness of propositional and predicate logic. We will cover the deduction theorem, the notions of consistency, decidability and independence. Toward the end of the course we'll be ready to look at some of the important limitative results such as the undecidability of first order logic, Gödel's incompleteness theorems and Tarski's indefinability theorem. The course is designed for advanced undergraduate students in philosophy and presupposes no special technical skills or background beyond what is studied in the prerequisite Introduction to Logic and Philosophical Logic in this department.

Text: Enderton, H, A Mathematical Introduction to Logic. 2nd edition. In addition, notes and handouts by the lecturer and any additional material will be posted on the course website.

Requirements: Attendance in lectures and Section is obligatory. Submission of at least 10 of the assigned problem sets is required for eligibility to take the final exam.

Grade: 85% final exam, 15% weekly problem sets.

Prerequisite: Introduction to Logic; Philosophical Logic.