NMAA13036U Introduction to Mathematical Logic

Knowledge: By the end of the course, the student is expected to be able to explain the concepts of: a first order language; of a model of a first order language; of formal deduction; of a computable relation and function; and finally, the student should be able to explain the meaning consistency and incompleteness of a theory, in particular as it relates to Peano Arithmetic.

Skills: By the end of the course, the student must be able to define the satisfacation relation, account for the axioms of the deductive system, define the notion of recursive function, and prove that a repository of common functions and relations are recursive, including the coding of basic syntactical notions. The student must be able to prove the key theorems of the course, such as the deduction theorem, the soundness theorem, and the first incompleteness theorem of Gödel.

Competences: Use of first order languages and structures in mathematics,  the formalization of proofs, the coding of syntactical notions in arithmetic. To explain the incompleteness phenomenon, and the method of diagonalization.