Set Theory, 88-202, 2018a



Hebrew lecture notes on basic Set Theory:

Lecture Topics
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.

p.s.
The corresponding Math-Wiki page is in here.