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. Download djvu Some papers including information on MK: 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. Download djvu
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: 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). Download djvu
Modal, paraconsistent etc. TBA

Finally, a bit of everything: