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250123 VO Special Topics in Set Theory (2021W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
MIXED
Moodle
Tu 05.10. 09:45-11:15 Seminarraum 10, Kolingasse 14-16, OG01

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).
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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

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.

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

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

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

Minimum requirements and assessment criteria

Examination topics

The material covered in the lectures.

Reading list

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.

Association in the course directory

MLOV

Last modified: Mo 13.09.2021 09:29