Set theory and metamathematics
The course covers the core of modern set theory, and independence results in set theory and proof theory.
Detailed description: Axioms of Zermelo–Fränkel set theory (ZF). Ordinals, well-orderings, and cardinal arithmetic. Independence of the axiom of choice and the continuum hypothesis: permutation models, forcing, and (optional) Gödel’s constructible universe. Gödel’s second incompleteness theorem. Sequent calculus, cut-elimination and normalisation. Gentzen’s consistency proof for Peano arithmetic. Interpretation and consequences of independence results.
The course consists of one element.
Teaching Format
Instruction consists of lectures and exercises.
Assessment
Assessment takes place through written exam and oral exam.
Examiner
The schedule will be available no later than one month before the start of the course.
We do not recommend print-outs as changes can occur. At the start of the course,
your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
K. Kunen, Set Theory, 1980, North-Holland Publishing
A.S. Troelstra, H. Schwichtenberg, Basic proof theory (2nd ed.), 2000, Cambridge University Press
Course reports are displayed for the three most recent course instances.
