Alternative Set Theories. January project @ ILLC, 2017.

Instructor: Yurii Khomskii

Schedule

References

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: Carolin Antos, Class Forcing in Class Theory Carolin Antos and Sy David Friedman, Hyperclass Forcing in Morse-Kelley Class Theory	Interesting online resources (with contributions by Joel David Hamkins and Victoria Gitman) Kelley-Morse set theory implies Con(ZFC) and much more Variants of Kelley-Morse set theory Questions on the consistency strength of MK
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: W. V. Quine, New Foundations for Mathematical Logic, American Mathematical Monthly, 44: 70-80. Ernst P. Specker, The Axiom of Choice in Quine's New Foundations for Mathematical Logic, Proceedings Nat. Acad. Science 1953. Roald Jensen, On the Consistency of a Slight (?) Modification of Quine's "New Foundations", Synthese, 19: 250-263. M. Randall Holmes, Quine's "New Foundations" is consistent, Preprint 2017.	Online resources: SEP entry on New Foundations
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.