Introduction to Mathematical Logic

Course content

First order logic, languages, models and examples. Formal deduction, deduction metatheorems, soundness, completeness and compactness, and applications of compactness. Basic axiomatic set theory, ordinals, cardinals, and the von Neumann hierarchy of sets, and its relation to the iterative concept of set.


MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Learning outcome

The participants are expected to acquire the knowledge listed above in the course description.

The participants are expected to be able to define the satisfacation relation, account for the axioms of the deductive system, and use the compactness theorem to construct models and counterexamples. 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. The student must be able to apply the theorem schema of recursion on the ordinals, and prove theorems by induction on the ordinals.

The participants are expected to master the most fundamental concepts and constructions in mathematical logic and axiomatic set theory, which are used in further studies in logic and set theory.

4 hours lecture and 3 hours tutorials per week for 7 weeks.

Example of course litterature:

H. Enderton: A Mathematical Introduction to Logic

Academic qualifications equivalent to a BSc degree in mathematics is recommended. At a minimum, the student should have completed courses equivalent to the first 2 full years of a mathematics BSc program offered by the Copenhagen Department of Mathematical Sciences, and must have taken DisMat, LinAlg, and Alg1.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Written assignment, 27 hours
Type of assessment details
Written take-home assignment 27 hours (9am Monday to 12pm Tuesday in week 8 of the block. If Monday is a holiday, the exam will start on a Tuesday instead, and end on a Wednesday).
Exam registration requirements

To be eligible to take the final exam the student must have handed in the 3 mandatory homework assignments, and these must all have been approved. One of these assignments will be a group assignment.

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

Same format as the ordinary exam, but taking place in the re-exam week.  If the 3 mandatory homework assignments were not approved before the ordinary exam they must be handed in for approval no later than 4 weeks before the Monday of the re-exam week.

Criteria for exam assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 146
  • Theory exercises
  • 21
  • Exam
  • 11
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 3
No limit
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Asger Dag Törnquist   (6-67796d6b787a4673677a6e34717b346a71)
Phone +45 35 32 07 57, office 04.2.17
Saved on the 28-02-2023

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