Knowledge Representation and Planning

Consequences of the Axiom of Choice Project 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 New System of Axioms Instead of ZF 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". Extending 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 axiomati… The Future of Set Theory by S. Shelah The Future of Set Theory by S. Shelah- The text of a talk given around the millennium. Axiom of Choice and Continuum Hypothesis Axiom of Choice and Continuum Hypothesis- Part of the Frequently Asked Questions in Mathematics. Set Theory Set Theory- Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech. Cantor's Theorem Cantor's Theorem- Article in the Platonic Realms, describing Cantor's diagonal argument that showed that 'infinite integers' can be ordered. Set Theory for the Working Mathematician Set Theory for the Working Mathematician- Krzysztof Ciesielski, CUP (1997). Contents and preface. Set Theorists Set Theorists- A list of email addresses and affiliations. Set Theoretic Analysis. Set Theoretic Analysis.- On a part of math where Set Theory, Topology and Analysis meet. Has surveys, preprints, conference announcements, book reviews and problems. Programming with Sets Programming with Sets- Using set-theoretic primitives as a conceptual tool in programming, includes discussion of SETL and MIRANDA languages. Bounded Set Theory Bounded Set Theory- A weak version of ordinary set theory using bounded quantification. Papers and software. New Foundations 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 loo… A Crash Course in the Mathematics of Infinite Sets A Crash Course in the Mathematics of Infinite Sets- A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory. The Beginnings of Set Theory The Beginnings of Set Theory- MacTutor History of Mathematics topic. Infinite Ink: The Continuum Hypothesis, by Nancy McGough Infinite Ink: The Continuum Hypothesis, by Nancy McGough- History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis. Shelah's Archive Shelah's Archive- Listing of all articles by Saharon Shelah, and links to many of them.