Syllabus
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.
Annotation
This is a follow up cours for the basic set theory course. Students will learn basic concepts of infinitary combinatorics and set theoretic topics beyond the fundamentals.