Syllabus
-Ordinal type of a well-ordered set, transfinite recursion, Zorn's lemma
-Ordinal arithmetics, Goodstein sequences
-Cardinal numbers and cardinal arithmetics
-Infinite Ramsey-type theorems
-Infinite graphs
-Applications of the axiom of choice in particular in combinatorics and geometry
Annotation
This course is a sequel to Set theory (NAIL063). We will focus mostly on combinatorial properties of infinite sets and graphs.
We will also see examples of "elementary" combinatorial statements whose validity depends on the chosen axioms. It is assumed that the students have basic knowledge of set theory (NAIL063), for some applications basics of group theory and measure theory would also be helpful.