|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.|
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