Directory of Set Theory Resources

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• A Crash Course in the Mathematics of Infinite Sets

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

• A New System of Axioms Instead of ZF

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

• Axiom of Choice and Continuum Hypothesis

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

• Bounded Set Theory

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

• Cantor's Theorem

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

• Consequences of the Axiom of Choice Project

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

• Extending Set Theory

  http://web.mit.edu/dmytro/www/NewSetTheory.htm
  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.

• Infinite Ink: The Continuum Hypothesis, by Nancy McGough

  http://www.ii.com/math/ch/
  History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis.

• New Foundations

  http://math.boisestate.edu/~holmes/holmes/nf.html
  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.

• Programming with Sets

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

• Set Theoretic Analysis.

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

• Set Theorists

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

• Set Theory

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

• Set Theory for the Working Mathematician

  http://www.math.wvu.edu/~kcies/STbook.html
  Krzysztof Ciesielski, CUP (1997). Contents and preface.

• Shelah's Archive

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

• The Beginnings of Set Theory

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

• The Future of Set Theory by S. Shelah

  http://front.math.ucdavis.edu/math.LO/0211397
  The text of a talk given around the millennium.

 

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