# NMAA13036U Introduction to Mathematical Logic

Volume 2020/2021
Education

MSc Programme in Mathematics

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.

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.

Example of course litterature:

H. Enderton: A Mathematical Introduction to Logic

Academic qualifications equivalent to a BSc degree is recommended.
4 hours lecture and 3 hours tutorials per week for 7 weeks.
• Category
• Hours
• Lectures
• 28
• Preparation
• 136
• Theory exercises
• 21
• Exam
• 21
• Total
• 206
Continuous feedback during the course of the semester
Credit
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.

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

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.