NMAA13036U  CHANGED: Introduction to Mathematical Logic

Volume 2018/2019

MSc Programme in Mathematics


First order logic, languages, models and examples. Formal deduction, deduction metatheorems, soundness, completeness and compactness, and applications of compactness. Basic axiomatic set theory, ordinals and cardinals. Towards the end of the course, other topics such as recursion theory, computable functions on the natural numbers, Turing machines, recursively enumerable sets, and arithmetization of first order syntax may be discussed.

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; arithmetization of first order syntax; the axioms of Zermelo-Fraenkel set theory; ordinals and cardinals.

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. The student must be able to prove the key theorems of the course, such as the deduction theorem, the soundness theorem, completeness theorem, and the compactness theorem.

Competences: Use of first order languages and structures in mathematics, the formalization of proofs, proof methods based on the compactness. Use ordinal analysis and transfinite recursion.

Example of course litterature:

H. Enderton: A Mathematical Introduction to Logic

4 hours lecture and 3 hours tutorials per week for 7 weeks.
7,5 ECTS
Type of assessment
Written assignment, 72 hours
Written take-home assignment 3 days (9am Monday to 9am Thursday in week
8 of the block.
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.

All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiners


Same format as the ordinary exam, but taking place in the re-exam week. If the 2 mandatory homework assignments were not approved before the ordinary exam they must be approved at the latest three weeks before the beginning of the re-exam week.

Criteria for exam assesment

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

  • Category
  • Hours
  • Lectures
  • 28
  • Theory exercises
  • 21
  • Preparation
  • 117
  • Exam
  • 40
  • Total
  • 206