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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.

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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)

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Last update : 21 April 2009