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).
|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.|
|11 March 2009.||Solutions: Barwise-Moss 6 (p.67-76).|
|18 March 2009.||Generic Extensions: Kunen VII.2 (p.186-192).|
|25 March 2009.||Exam Week. No classes.|
|1 April 2009.||Forcing: Kunen VII.3 (p.192-201).|
|8 April 2009.||Bisimulation: Barwise-Moss 7 (p.77-90).|
|15 April 2009.||Substitution: Barwise-Moss 8 (p.91-102).|
|22 April 2009.||The generic extension is a model of set theory: Kunen VII.4
|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).|
|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)