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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.

Cantor's 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
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.

Equivalence Relation
Encyclopedia entry on equivalence relations and their role in 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.

The Mathematics of Set Theory
Detailed description of parts of introductory set theory.

Metamath Proof Explorer
Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms.

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.

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".

Operational Set Theory
Description, errata and reviews of a book by Luis E. Sanchis.

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.

Set Theorists
A list of email addresses and affiliations.

Set Theory
Directory of set theorists, maintained by Jean A. Larson.

Set Theory
Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.

Set Theory
From Dave Rusin's "Known Math" collection.

Set Theory for the Working Mathematician
Krzysztof Ciesielski, CUP (1997). Contents and preface.

Set Theory Page
Collection of links related to set theory.

Sets and Their Sizes
An alternative to Cantor's theory of cardinality. Dissertation by Fred M. Katz.

Shelah's Archive
Listing of all articles by Saharon Shelah, and links to many of them.


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