Universität Wien

250123 VO Special Topics in Set Theory (2022W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
VOR-ORT
Moodle

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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)

Art der Leistungskontrolle und erlaubte Hilfsmittel

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

Mindestanforderungen und Beurteilungsmaßstab

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

Prüfungsstoff

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.

Literatur

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).

Zuordnung im Vorlesungsverzeichnis

MLOV

Letzte Änderung: Di 07.02.2023 16:09