NMAA13036U Introduction to Mathematical Logic
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, cardinals, and the von Neumann hierarchy of sets, and its relation to the iterative concept of set.
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.
Example of course litterature:
H. Enderton: A Mathematical Introduction to Logic
- Theory exercises
- 7,5 ECTS
- Type of assessment
- Written assignment, 72 hoursWritten 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 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 assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.