Universität Wien

250035 VO Introduction to Descriptive Set Theory (2026S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Dienstag 03.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 05.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 10.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 17.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 19.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 24.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 26.03. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 14.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 16.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 21.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 23.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 28.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 30.04. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 05.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 07.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 12.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 19.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 21.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 26.05. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 02.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 09.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 11.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 16.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 18.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 23.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 25.06. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

This course introduces the main ideas and techniques of Descriptive Set Theory and their applications in analysis, set theory, and combinatorics. The aim is to familiarize students with the structure and complexity of definable sets of real numbers and related spaces, and to develop the tools used to study them.

The course will be organized into three parts. The first and longest part will cover classical descriptive set theory, including the theory of Borel and analytic sets, Baire category methods, and infinite two-player games, with emphasis on their connections to and applications in analysis. The second part will describe interactions with set theory, including topics such as Shoenfield absoluteness, the limitations of ZFC in resolving questions about the projective hierarchy, and the role of large cardinals in addressing these problems. The final part will present selected modern developments, such as results from Borel combinatorics and/or invariant descriptive set theory.

Art der Leistungskontrolle und erlaubte Hilfsmittel

There will be a final exam during the last lecture. A couple more exam dates will be announced later, to take place during the winter semester of 2026.

Mindestanforderungen und Beurteilungsmaßstab

Pass the final exam.

Prüfungsstoff

For the final exam you will need to know the material covered in the lecture and be able to apply it. Problems will be assigned regularly through the lectures and the discussion sessions. You should expect similar problems to appear on the final.

A good way to practice is by solving problems from this list:
https://www.math.mcgill.ca/atserunyan/Teaching_notes/dst_problems.pdf

Literatur

I will be posting handwritten notes on a weekly or bi-weekly basis.
Parts of these notes will be based on a combination of the following sources:

(1) Alexander S. Kechris "Classical Descriptive Set Theory"

(2) Anush Tserunyan's Notes: https://www.math.mcgill.ca/atserunyan/Teaching_notes/dst_lectures.pdf

Zuordnung im Vorlesungsverzeichnis

MLOV; ML1; MEL

Letzte Änderung: Di 06.10.2026 10:07