Axiomatic Set Theory
(Spring 2018, ILLC, University of Amsterdam)
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Format
Lectures and tutorial classes. There will be lectures on Tuesdays and on some Fridays; and workcollege classes in all other Fridays..
Prerequisites: Knowledge of the basics of propositional and first-order logic (e.g. propositional connectives, truth tables, quantifiers and their laws). Mathematical maturity: the facility to handle mathematical notation, concepts and techniques, and the ability to quickly learn new such concepts and techniques and to immediately use them to prove new results upon demand and solve exercises that built on this newly acquired knowledge.
Warnings:
Deadlines for homeworks are strict, no delays are allowed,
Study materials
The main textbooks for this course are
K. Devlin, The Joy of Sets, Springer-Verlag, 1993 (Second Edition);
R. M. Smullyan and M. Fitting, Set Theory and the Continuum Problem, Dover Publications, Inc., 2010.
(This is a revised/corrected edition of the 1996 Oxford University Press book with the name/authors, but you can also use the original 1996 edition, since errors are few and minor).
For other technical material, I might sometimes use
K. Kuratowski and A. Mostowski, Set Theory, Studies in Logic and Foundations of Mathematics vol. 86. North-Holland Publishing Company , 1976 (Second Edition)
but it is not necessary for students to look at this (unless they are really interested in acquiring more advanced technical knowledge of set theory, going beyond this course).
For a biography of Georg Cantor, click HERE ,or look up
J. W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press, 1979
for a more detailed biography and philosophical discussion.
For more on the philosophical foundations of Set Theory, see the excellent discussion in
M. Hallett, Cantorian Set Theory and Limitation of Size, Oxford University Press, 1984 (reprinted in paperback, 1986, 1988)
or also
M. Potter, Set Theory and Its Philosophy, Oxford University Press, 2004 (reprinted, 2009).
In addition, I will of course have slides of lectures, that I will post on this page (and if possible on Blackboard). Though there will be many proofs and details that will be done only using chalk and blackboard, so attendance is strongly encouraged!