Basic course about set theory: starting with axioms of ZFC, covering ordinals, cardinals, axiom of choice, and ending with
infinitary combinatorics.
Motivating pictures:
 1. class 22.2.2017

Motivation: contradictions in the naive set theory. Starting with the axioms of ZermeloFraenkl: Axioms of Existence, Extensionality,
Axiom Scheme of Comprehension. $x \in \emptyset$
Somewhat detailed notes from the class.
(Notes are written using a nice app called Workflowy.)
Exercises
 Prove that the "set of all sets" does not exists. [Hint: if it does, use the Axiom Scheme of Comprehension and deduce a contradiction, as we did in class.]
 Assume a weaker version of the Axiom of Existence: A set exists. Use the Comprehension Schema to deduce the version we started with.
[Hint: If $A$ is a set, consider $\{x \in A \mid x \not= x \}$.]
 2. class 1.3.2017

More axioms: The Axiom of Pair, The Axiom of Union, and The Axiom of Powerset. Ordered pair. Relations, existence of cartesian product, etc.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 3. class 8.3.2017

Building the natural numbers using inductive sets and the Axiom of Infinity. Proving induction, etc.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 4. class 15.3.2017

Recursive definitions, arithmetics.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 5. class 22.3.2017

Cardinality of sets. CantorBernstein. Finite sets.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 6. class 29.3.2017

Countable sets. Cantor theorem and uncountability of reals.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 7. class 5.4.2017

Dedeking cuts. Cardinal numbers.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 8. class 12.4.2017

Wellordered sets. Ordinals (beginning).
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 9. class 19.4.2017

More ordinals.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 10. class 26.4.2017

Plan: arithmetic of ordinals.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
The notes include a detailed proof of the theorem about addition of ordinals, that perhaps seemed too complicated in class.
 11. class 3.5.2017

How to use ordinals define cardinals.
Axiom of choice  various forms and applications.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 12. class 10.5.2017

Applications of AC. Infinite Ramsey theorem.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.
 no class on 17.5.2017

All classes canceled  sporting day.
 no class on 24.5.2017

I cannot attend this day, unfortunately. (Sorry for any complications this may cause.)
 13. class on 25.5.2017  usual time (17:2018:50) in S9

More infinite combinatorics: uncountable Ramsey, trees, Konig's lemma with applications.
Somewhat detailed notes from the class. Do not miss the Exercises at the end of the notes.