Dr Benedikt Loewe & Dr Yde Venema: Seminar on Mathematical Logic (2nd Semester 2008/2009)

Seminar on Mathematical Logic
2008/2009; 2nd Semester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructors: Dr Benedikt Löwe, Dr Yde Venema
Time: Wednesday, 17-19
Place: P.018
ECTS credit points: 3
Course language: English
Intended Audience: M.Sc. students of Logic and Mathematics
Course Description: UvA Studiegids

The topics of this semester are model constructions in set theory: forcing and non-wellfounded set theory. The part on forcing continues last semester's course on set-theoretic model constructions taught by Khomskii, Löwe and Semmes. Students giving a presentation in this part should have followed this course or should have equivalent background knowledge. The part on non-wellfounded set theory requires no prior knowledge other than basic knowledge in axiomatic set theory (less than is typically covered in our course Axiomatische Verzamelingentheorie).

Study material.

Kenneth Kunen, Set Theory, An Introduction to Independence Proofs, Amsterdam 1980 [Studies in Logic and the Foundations of Mathematics 102]
Jon Barwise, Lawrence Moss, Vicious Circles, Stanford CA 1996 [CSLI Lecture Notes 60]
Peter Aczel, Non-well-founded sets, Stanford CA 1988 [CSLI Lecture Notes]

All of the books will be on reserve in the library for students to xerox the relevant pages for their talks.

Classes:

11 February 2009.	Introductory Meeting.
18 February 2009.	Class cancelled
25 February 2009.	Martin's Axiom: Kunen II.2 (p.51-55). Pablo Cubides Kovacsics.
4 March 2009.	Measurable Cardinals and Elementary Embeddings. Karl Heuer.
11 March 2009.	Solutions: Barwise-Moss 6 (p.67-76). Yves Fomatati.
18 March 2009.	Generic Extensions: Kunen VII.2 (p.186-192). Herman Stel.
25 March 2009.	Exam Week. No classes.
1 April 2009.	Forcing: Kunen VII.3 (p.192-201). Yurii Khomskii.
8 April 2009.	Bisimulation: Barwise-Moss 7 (p.77-90). Matthew Wampler-Doty.
15 April 2009.	Substitution: Barwise-Moss 8 (p.91-102). Raul Leal.
22 April 2009.	The generic extension is a model of set theory: Kunen VII.4 (p.201-204). Evan DeCorte.
29 April 2009.	Building a model of ZFA: Barwise-Moss 9 (p.102-116). Sam van Gool.
6 May 2009.	Class cancelled
13 May 2009.	Building a model of ZFC+ -CH: Kunen VII.5 (p.204-211). Rogier Jacobsz.
20 May 2009.	Additional topics.
27 May 2009.	Exam Week. No classes.

Possible additional topics for the final two weeks:
More general forcings: Kunen VII.6 (p.211-217); Applications in Modal Logic: Barwise-Moss 11 (p.119-158)

Last update : 21 April 2009