NMAA13036U Introduction to Mathematical Logic

Volume 2014/2015
Content

First order logic, languages, models and examples. Recursion theory, computable functions on the natural numbers, Turing machines, recursively enumerable sets and Turing degrees. Gödel's incompleteness theorems.

Learning Outcome

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.

4 hours lecture and 3 hours tutorials per week for 7 weeks.
  • Category
  • Hours
  • Colloquia
  • 21
  • Exam
  • 40
  • Excursions
  • 2
  • Guidance
  • 4
  • Lectures
  • 28
  • Preparation
  • 70
  • Project work
  • 20
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 min
With preparation time
Exam registration requirements
To be eligible to take the final exam the student must have handed in the 2 mandatory homework assignments, and these must both have been approved and have received a passing grade.
Aid
Only certain aids allowed

Notes and the text book.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.