Universität Wien
Warning! The directory is not yet complete and will be amended until the beginning of the term.

250123 VO Special Topics in Set Theory (2022W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Register/Deregister for this course

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 04.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 06.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 11.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 13.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 18.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 20.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 25.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 27.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 03.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 08.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 10.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 15.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 17.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 22.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 24.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 29.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 01.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 06.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 13.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 15.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 10.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 12.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 17.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 19.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 24.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Thursday 26.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Tuesday 31.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01

Information

Aims, contents and method of the course

This lecture will devote itself to the classical arithmetic of singular cardinals. We will give an introduction to the basic definitions and results on cardinal arithmetic, the continuum hypothesis and the method of forcing. Our goal is to understand how arithmetic on singulars differs from the arithmetic on regulars, as well as to study classical forcing constructions controlling the continuum function at specific singulars. At the end, we want to give a gently introduction to the theory of possible cofinalities of Shelah. Here a tentative program:

I. Review of basic concepts- cardinality and cofinality.
1. König's Theorem. Exponentiation of cardinals. GCH.
2. A short review on forcing.
3. Easton's theorem.

II. Arithmetic of singular cardinals.
1. The singular cardinal hypothesis.
2. Silver's Theorem.
3. Galvin-Hajnal’s theorems.

III. Large cardinals and the singular cardinals problem.
1. Elementary embeddings and some large cardinal notions.
2. Measurable cardinals and supercompact cardinals.
3. Silver's forcing.
4. Prikry forcing.

IV. Prikry-type forcings.
1. Adding many Prikry-sequences.
2. Nice systems of ultrafilters.
3. Collapsing cardinals.
4. Down to $\aleph_\omega$.

V. A gently introduction on pcf (time availability dependent)

Assessment and permitted materials

Written assignments: 50 points
Oral presentation: 20 points
Final exam: 30 points

Minimum requirements and assessment criteria

1: 85-100 Points
2: 70-84 Points
3: 55-69 Points
4: 40-54 Points
5: 0-39 Punkte

Examination topics

Each student will have an oral presentation (topics to be agreed).
There will be weekly notes. Its content is the base for the weekly assignments and the final exam.

Reading list

1. Akihiro Kanamori. The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings.
2. Kenneth Kunen, Set Theory (North Holland, 1980), particularly for independence proofs.
3. Thomas Jech, Set Theory: The Third Millenium Edition (Springer 2003).

Association in the course directory

MLOV

Last modified: Tu 07.02.2023 16:09