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Logic and Foundations
Open Directory - Science: Math: Logic and Foundations: Set Theory
The Axiom of Choice
- This page gives a brief explanation of the Axiom of Choice and links to other related websites.
Axiom of Choice and Continuum Hypothesis
- Part of the Frequently Asked Questions in Mathematics.
The Beginnings of Set Theory
- MacTutor History of Mathematics topic.
Bounded Set Theory
- A weak version of ordinary set theory using bounded quantification. Papers and software.
- 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
- Project to keep the book (also named in the title), describing forms related to the Axiom of Choice and their implications, updated.
A Crash Course in the Mathematics of Infinite Sets
- A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory.
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.
The Future of Set Theory by S. Shelah
- The text of a talk given around the millennium.
Infinite Ink: The Continuum Hypothesis, by Nancy McGough
- History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis.
- 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.
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".
Programming with Sets
- Using set-theoretic primitives as a conceptual tool in programming, includes discussion of SETL and MIRANDA languages.
Set Theoretic Analysis.
- On a part of math where Set Theory, Topology and Analysis meet. Has surveys, preprints, conference announcements, book reviews and problems.
- A list of email addresses and affiliations.
- From Dave Rusin's "Known Math" collection.
- Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.
Set Theory for the Working Mathematician
- Krzysztof Ciesielski, CUP (1997). Contents and preface.
- Listing of all articles by Saharon Shelah, and links to many of them.
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