Department of Mathematics
Homepages
(hier geht es zur ggf. vollständigeren Homepage im alten Layout)
(this way to the possibly more complete Homepage in the old layout)
Doodle for planning first meeting: https://doodle.com/poll/92q2ebr5p6nc86m6
Google form for topic distribution: https://goo.gl/forms/naConOkOq24ENqjj1
The slides to the introductory presentation.
Finally, a bit of everything:
(this way to the possibly more complete Homepage in the old layout)
Alternative Set Theories. January project @ ILLC, 2017.
Instructor: Yurii Khomskii
Doodle for planning first meeting: https://doodle.com/poll/92q2ebr5p6nc86m6
Google form for topic distribution: https://goo.gl/forms/naConOkOq24ENqjj1
The slides to the introductory presentation.
Schedule
Date & Time | Who | What | Where | Final Report: |
Wed 10 Jan, 18:00 - 20:00 | Yurii Khomskii | Introductory meeting | F1.15 (Seminar room) | |
Thu 25 Jan, 15:00 - 17:00 | Ethan Lewis | New Foundations (NF) | F2.19 (SP-107) | Ethan's report |
Fri 26 Jan, 11:00 - 13:00 | Robert Passmann | Modal Set Theory | F3.20 (SP-107) | |
Mon 29 Jan, 11:00 - 13:00 | Davide Quadrellaro | Class Theories (NGB & MK) | F2.19 (SP-107) | Davide's report |
Mon 29 Jan, 15:00 - 17:00 | David Santamaria Legarda | Class conceptions of Penelope Maddy | F2.19 (SP-107) | David's report |
Tue 30 Jan, 11:00 - 13:00 | Romain Grausi | Non-well-founded Set Theory (AFA) | F1.15 (Seminar room) | Romain's report |
Tue 30 Jan, 15:00 - 17:00 | Adrien Champougny | Kripke-Platek (KP) | F1.15 (Seminar room) | Adrien's report |
Wed 31 Jan, 11:00 - 13:00 | Nuno Filipe | Philosophy of paraconsistent mathematics (G. Priest) | F1.15 (Seminar room) | Nuno's report Handout |
Wed 31 Jan, 15:00 - 17:00 | Hrafn Oddsson | Paraconsistent Set Theory | F1.15 (Seminar room) | Hrafn's report |
Thu 1 Feb, 11:00 - 13:00 | Raja Damanik | Intuitionistic/Constructive Set Theory | F1.15 (Seminar room) | |
Thu 1 Feb, 15:00 - 17:00 | Sam Adam-Day | Advanced topics in IZF/CZF | F1.15 (Seminar room) | Sam's report |
References
The references are intended as suggestions, but (since the aim of this project is in part to teach independent research skills) you are more than welcome to look for additional sources.
NGB | Elliott Mendelson, Introduction to Mathematical Logic, Chapter 4 | |||
MK | See above, Chapter 4, Secion 6 | John L. Kelley, General Topology, Appendix. | Some papers including information on MK:
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Interesting online resources (with contributions by Joel David Hamkins and Victoria Gitman) |
KP | Jon Barwise, Admissible Sets and Structures | Keith Devlin, Constructibility, Section I.11. | ||
NF | T. E. Forster, Set Theory with a Universal Set; Exploring an Untyped Universe | Randall Holmes, Elementary Set Theory with a Universal Set | Some papers dealing with NF:
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Online resources: |
CZF and IZF | Peter Aczel and Michael Rathjen, CST Book draft (2010) | Peter Aczel and Michael Rathjen, Notes on Constructive Set Theory (2001) | ||
Anti-foundation | Peter Aczel, Non-well-founded sets | Keith Devlin, The Joy of Sets; Fundamentals of Contemporary Set Theory, Chapter 7 (Springer-Verlag 1994). | ||
Modal, paraconsistent etc. | TBA |
Finally, a bit of everything:
- M. Randall Holmes, Thomas Forster and Thierry Libert, Alternative Set Theories, Handbook of the History of Logic: Sets and Extensions in the Twentieth Century, 2012.