INF9840 - Computability theory

Schedule, syllabus and examination date

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Course content

This course gives an introduction to classic computability theory (also known as recursion theory). The course covers the following topics:  primitive recursion,  computable functions and computable indices, semi-computable and computably enumerable sets and undecidability.

Learning outcome

We will use the computability theory we develop to prove:

- Undecidability of the halting problem

- Undecidability of the Entscheidungsprobem

- Godel's First Incompleteness Theorem

We will also discuss the negative solution of Hilbert's 10th problem.

Basic skills in theoretical computer science and in-depth skills in computability theory.

This course will include one of the three advanced topic.The choice of topic will be based on the students' interests. Some options are:
- subrecursive hierarchies
- computability of real numbers
- Turing degrees.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Overlapping courses

10 credits overlap with INF5840 - Computability theory


Two lectures a week


Written or oral exam. No mandatory assignments prior to the exam.

Examination support material

No examination support material is allowed.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course






Spring 2015, 217


When the course is given

Teaching language