ADVANCED LOGIC: METATHEORY
This course will demonstrate some of the fundamental metatheoretical results about classical logic. These include the soundness, completeness, and undecidability of first-order logic. Along the way, we cover some basics of computability theory. This prepares us to give an overview of Gödel's well-know incompleteness results. We finish by discussing some considerations from second-order logic.
Exercise sets, one mid term, and one final examination.
Week 1: Sets, relations and functions
Week 2: First-order logic: syntax
Week 3: First-order logic: semantics
Week 4: Theories and their models
Week 5: Derivation systems
Week 6: Sequent calculus
Week 7: Natural deduction
Week 8: Completeness
Week 9: Turing machine computations
Week 10: Undecidability
Week 11: Incompleteness
Week 12: Second-order logic