Syllabus
The seminar will cover approximately the topics of Chapter III of the book Balcar, Štěpánek: Teorie množin. The selection and depth of topics covered will be adjusted according to the interests of seminar participants.
Topics: constructible sets, independent partitions, Hewit-Marczewski-Pondiczery theorem, almost disjoint systems, Δ-system lemma, theorem on free sets, stationary sets and Fodor's lemma, Ulam matrix, Silver's theorem, combinatorial principles diamond and square, uncountable linear orders, Suslin line and Suslin tree, Kurepa tree, Aronszajn trees, Ramsey theorem and its canonical version, partition relations, Galvin-Prikry theorem, Erdös-Dushnik-Miller theorem, Erdös-Rado theorem, large cardinals.
Annotation
This is a follow up seminar for the basic set theory course. Students will form a study group to learn basic concepts of infinitary combinatorics and set theoretic topics beyond the fundamentals. Seminar is suitable for students of 2nd and 3rd year of bachelor program who want to pursue topics in abstract mathematics.
The seminar may be tough in English.