To introduce students to the formal notions of language, proof, semantics, and completeness with quantificational logic, in order to: • improve their understanding and appreciation of the foundations of mathematics and • provide the necessary background knowledge for later logic course units

Introduction. Review of propositional logic. Motivation for the study of predicate logic with examples of reasoning with quantifiers. Truth. Languages for predicate logic. Signatures and structures. Formulae, sentences and Tarski's definition of Truth. Logical consequence, logical equivalence and logical validity. Theories and models. Proof. An axiom system for predicate logic. The Soundness Thoerem. Consistency. Completeness. The completeness theorem for predicate logic. Simple applications.