This class will provide cover the foundational results of modern formal logic. We will begin by studying proofs for propositional logic. Then we will learn about models for propositional logic, which raises the questions about how these two things, proofs and models, relate. We prove that they align for classical logic in the form of the soundness and completeness theorems. From there, we will have a short introduction to some important modal logics, logics which formalize the concepts of necessity and possibility. We will learn about their models and proofs, as well as soundness and completeness results. Next, we will study models and proofs for quantifiers, connectives that allow us to make general claims about objects. This will culminate in completeness result for first-order logic. The remainder of the course will be spent building to Goedel’s incompleteness theorems, showing that strong theories of formal arithmetic are incomplete. There are certain arithmetic claims that are undecidable using those theories.