Universität Wien
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250123 VO Special Topics in Set Theory (2021W)

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

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

Depending on the ongoing situation involving the pandemic the lectures will be some combination of in person, hybrid and on Zoom, with the precise make up subject to change as necessary.

The Zoom link, if and when we meet on Zoom, will be available on the Moodle course page. You may also write to corey.bacal.switzer@univie.ac.at to obtain it.

  • Dienstag 05.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 07.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 12.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 14.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 19.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 21.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 28.10. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 04.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 09.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 11.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 16.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 18.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 23.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 25.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 30.11. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 02.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 07.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 09.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 14.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 16.12. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 11.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 13.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 18.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 20.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 25.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 27.01. 09:45 - 11:15 Seminarraum 10, Kolingasse 14-16, OG01

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

This is a more advanced course in set theory, picking up where Axiomatic Set Theory from last semester left off. The focus of the course is on the method of forcing and its applications. We will be particularly interested in iterated forcing and its applications to problems in topology, analysis and combinatorics. Most important among these will be the study of classical cardinal characteristics such as b, d, a and the cardinals associated with the ideals of meager and measure zero sets. We will also discuss Martin's axiom and the independence of Souslin's hypothesis.

It is strongly recommended that students of this course also attend Professor Fischer's Research Seminar in Set Theory.

Art der Leistungskontrolle und erlaubte Hilfsmittel

A final oral exam or regular class participation in the form of assignments.

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

The material covered in the lectures.

Literatur

1) Lecture notes of the course

2) Uri Abraham, "Proper Forcing", in Handbook of Set Theory, Foreman, Kanamori, and Magidor (eds.), Springer, 2010, pp.333-394.

3) T. Bartoszynski and H. Judah, "Set Theory: On the Structure of the Real Line". A.K. Peters, Wellsley, MA, 1995. x+546pp.

4) L. Halbeisen, "Combinatorial Set Theory with a Gentle Introduction to Forcing", Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2017. xvi+594pp.

5) T. Jech, "Set Theory", The Third millennium edition, revised and expanded. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003. xiv + 769pp.

6) K. Kunen, "Set Theory", Studies in Logic, Mathematical Logic and Foundations Vol. 34. Revised Edition. College Publications, London, 2013. viii + 402pp.

7) S. Shelah, "Proper and Improper Forcing", Second Edition. Perspectives in Logic, Cambridge University Press, Cambridge, 2016. xlviii+1020pp.

Zuordnung im Vorlesungsverzeichnis

MLOV

Letzte Änderung: Mi 15.06.2022 17:09