This semester, the Set Theory seminar runs Thursdays, 10--12, building 604, room 103.
The course on Walks on Ordinals runs Thursdays, 13--16, building 105, room 4.
Note: Due to a conference, the first meeting will take place on the second week of the semester.
Hebrew lectures notes on basic Set Theory:
|Lecture #1||Partial orders. The Rasiowa-Sikorski Lemma. Every countable dense linearly ordered set without endpoints is order-isomorphic to the rational line.|
|Lecture #2||Transitive sets. Well-orders are rigid. The class of ordinals is well-ordered.|
|Lecture #3||Every two well-ordered sets are compatible. Finite ordinals. Every well-ordered set is isomorphic to a unique ordinal. Ordinals arithmetic: sums and multiplications.|
|Lecture #4||Transfinite induction, and applications to ordinal arithmetic. Ordinal power.|
|Lecture #5||Hartogs' number. Definition by recursion. The axiom of choice. Zermelo's well-ordering principle. Hausdorff's maximality principle. Zorn's lemma. Hartogs' comparability of cardinals. Tychonoff's theorem.|
|Lecture #6||The axioms of ZFC. The effect of AC on infinite graph theory: the Shelah-Soifer graph, and the Komjath-Galvin graph.|
|Lecture #7||ZF implies that Hartogs' number is indeed a set. Cardinals, and cardinal arithmetic. Cantor's theorem.|
|Lecture #8||kxk=k for every infinite cardinal k, and applications to cardinal arithmetic. Successor and limit cardinals. The Aleph function. Cofinality of partially ordered-sets. Regular and singular cardinals. Every successor cardinal is regular.|
|Lecture #9||Analysis of the Aleph function: cofinality, surjectivity, fixed points. Some more cardinal arithmetic, including Konig's lemma and Hausdorff's formula.|
|Lecture #10||Cardinal arithmetic assuming GCH. Strong limit cardinals and the Beth function. Ideals. The nonstationary ideal is sigma-additive. Normal functions. Closed and unbounded sets. Appendix on Ramsey's theorem.|
|Lecture #11||Filters. CUB is the dual of NS. Diagonal union. The nonstationary ideal is normal. Fodor's lemma. Ulam's matrix.|
|Lecture #12||Every stationary subset of w1 may be partitioned into w1 many pairwise disjoint sets. Partition calculus for dimension one. Partition calculus for dimension two: the Sierpinski coloring. The Delta-system lemma.|
|Lecture #13||Set-theoretic implementation of the classic system of numbers: natural numbers, integers, rational numbers, the real line (Dedekind cuts). Order-theoretic uniqueness of the real line. Cardinality of the real line.|