Title of the course:
Set theory (BSc)
Number of contact hours per week:
Credit value:
Course coordinator(s):
Department(s):
Evaluation:
Prerequisites:
2+0
2+0
Péter Komjáth
Department of Computer Science
oral examination
A short description of the course:
Naive and axiomatic set theory. Subset, union, intersection, power set. Pair, ordered pair,
Cartesian product, function. Cardinals, their comparison. Equivalence theorem. Operations
with sets and cardinals. Identities, monotonicity. Cantor’s theorem. Russell’s paradox.
Examples. Ordered sets, order types. Well ordered sets, ordinals. Examples. Segments.
Ordinal comparison. Axiom of replacement. Successor, limit ordinals. Theorems on
transfinite induction, recursion. Well ordering theorem. Trichotomy of cardinal comparison.
Hamel basis, applications. Zorn lemma, Kuratowski lemma, Teichmüller-Tukey lemma.
Alephs, collapse of cardinal arithmetic. Cofinality. Hausdorff’s theorem. Kőnig inequality.
Properties of the power function. Axiom of foundation, the cumulative hierarchy. Stationary
set, Fodor’s theorem. Ramsey’s theorem, generalizations. The theorem of de Bruijn and
Erdős. Delta systems.
Textbook:
A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.
Further reading: