Set Theory

The Axiom of Choice
This page gives a brief explanation of the Axiom of Choice and links to other related websites.
http://math.vanderbilt.edu/~schectex/ccc/choice.html

Axiom of Choice and Continuum Hypothesis
Part of the Frequently Asked Questions in Mathematics.
http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node34.html

The Beginnings of Set Theory
MacTutor History of Mathematics topic.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html

Bounded Set Theory
A weak version of ordinary set theory using bounded quantification. Papers and software.
http://www.botik.ru/~logic/bst/bst.html

Cantor's Theorem
Article in the Platonic Realms, describing Cantor's diagonal argument that showed that 'infinite integers' can be ordered.
http://www.mathacademy.com/pr/prime/articles/cantor_theorem/

Consequences of the Axiom of Choice Project
Project to keep the book (also named in the title), describing forms related to the Axiom of Choice and their implications, updated.
http://www.math.purdue.edu/~jer/cgi-bin/conseq.html

A Crash Course in the Mathematics of Infinite Sets
A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory.
http://www.earlham.edu/~peters/writing/infapp.htm

Equivalence Relation
Encyclopedia entry on equivalence relations and their role in set theory.
http://www.iscid.org/encyclopedia/Equivalence_Relation

Extending Set Theory
Extends the language of set theory through restricted self-reference and through certain large cardinals. Also discusses higher order set theory and axiomatization through reflection principles.
http://web.mit.edu/dmytro/www/NewSetTheory.htm

The Future of Set Theory by S. Shelah
The text of a talk given around the millennium.
http://front.math.ucdavis.edu/math.LO/0211397

Infinite Ink: The Continuum Hypothesis, by Nancy McGough
History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis.
http://www.ii.com/math/ch/

Metamath Proof Explorer
Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms.
http://www1.shore.net/~ndm/java/mm.html

New Foundations
Set theory introduced by W. V. O. Quine in 1937. This is a refinement of Russell's theory of types based on the observation that the types in Russell's theory look the same, as far as one can apparently prove.
http://math.boisestate.edu/~holmes/holmes/nf.html

A New System of Axioms Instead of ZF
The page claims that "the axioms shown below have the contents that should overturn the set theory of today".
http://hp.vector.co.jp/authors/VA011700/math/wardwww.htm

Operational Set Theory
Description, errata and reviews of a book by Luis E. Sanchis.
http://www.cis.syr.edu/~sanchis/operational.html

Programming with Sets
Using set-theoretic primitives as a conceptual tool in programming, includes discussion of SETL and MIRANDA languages.
http://www.cs.nmsu.edu/~complog/sets/

Set Theoretic Analysis.
On a part of math where Set Theory, Topology and Analysis meet. Has surveys, preprints, conference announcements, book reviews and problems.
http://www.math.wvu.edu/~kcies/STA/STA.html

Set Theorists
A list of email addresses and affiliations.
http://www.cs.elte.hu/~kope/setad

Set Theory
Directory of set theorists, maintained by Jean A. Larson.
http://www.math.ufl.edu/~jal/set_theory.html

Set Theory
Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.
http://plato.stanford.edu/entries/set-theory/

Set Theory
From Dave Rusin's "Known Math" collection.
http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

Set Theory for the Working Mathematician
Krzysztof Ciesielski, CUP (1997). Contents and preface.
http://www.math.wvu.edu/~kcies/STbook.html

Set Theory Page
Collection of links related to set theory.
http://www.cis.syr.edu/~sanchis/setory.html

Sets and Their Sizes
An alternative to Cantor's theory of cardinality. Dissertation by Fred M. Katz.
http://www.logicandlight.com/projects/Infinity/SetsAndSizes.pdf

Shelah's Archive
Listing of all articles by Saharon Shelah, and links to many of them.
http://shelah.logic.at/