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.

Education

MSc Programme in Mathematics

Learning outcome

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

Skills: 
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.

Competences: 
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 is recommended.

Continuous feedback during the course of the semester
ECTS
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.)
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 136
  • Theory exercises
  • 21
  • Exam
  • 21
  • English
  • 206