Introduction to Mathematical Logic
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
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.
- 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).
- 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)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 3
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Asger Dag Törnquist (6-6b7d716f7c7e4a776b7e7238757f386e75)
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Courseinformation of students