G8 backs financial reform summit

The G8 leaders agree to hold a summit with other states to discuss global financial reform, and reopen trade negotiations.

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Watchdog sorry for bank failings

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news.bbc.co.uk

Scientists discover ray of hope for the red squirrel

Some red squirrels have developed immunity to a deadly disease carried by grey squirrels, scientists find.

news.bbc.co.uk

Send your video, pictures and story ideas

Have you got a good story? BBC News wants to hear from you.

news.bbc.co.uk

'Easy prey'

Bomber's mother says he was 'brainwashed'

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Recession fears knock US shares

Wall Street shares plummet on fresh fears of a global recession despite moves to strengthen the financial system.

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'Bomb material purchase' on CCTV

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US rivals to spar in final debate

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Madonna and Ritchie confirm split

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Man admits botched bomb attack

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Ballesteros stable after surgery

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BBC evicts top shows from London

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Three-year police pay deal struck

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UK soldier killed in Afghan blast

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 World Catalog > Science > Math > Logic and Foundations > Set Theory

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World Catalog > Science > Math > Logic and Foundations > Set Theory

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

Graand

Free Classified Ads Portal

www.graand.com

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/

Blue Peter at 50

A look back at some of the iconic show's highlights

news.bbc.co.uk

Send your video, pictures and story ideas

Have you got a good story? BBC News wants to hear from you.

news.bbc.co.uk

BBC evicts top shows from London

The BBC moves The Weakest Link and Newsnight Review to Glasgow as part of a plan to make sure it represents all of the UK.

news.bbc.co.uk

Progress made in teacher strike

The two sides at the centre of a strike at Movilla High School in Newtownards are to attend talks at the Labour Relations Agency.

news.bbc.co.uk

UK soldier killed in Afghan blast

A British soldier has been killed in an explosion in southern Afghanistan, the Ministry of Defence says.

news.bbc.co.uk

G8 backs financial reform summit

The G8 leaders agree to hold a summit with other states to discuss global financial reform, and reopen trade negotiations.

news.bbc.co.uk

'Easy prey'

Bomber's mother says he was 'brainwashed'

news.bbc.co.uk

Germany 1-0 Wales

Wales slip to a narrow defeat against Germany their in 2010 World Cup qualifying Group Four game in Monchengladbach.

news.bbc.co.uk

Butcher battles 'no chopping or singing in the morning' order

An east London butcher battles his local council after he was ordered to stop chopping and singing in the morning.

news.bbc.co.uk

Ballesteros stable after surgery

Golf legend Seve Ballesteros is in a stable condition after undergoing an operation on a brain tumour.

news.bbc.co.uk

Three-year police pay deal struck

A new three-year pay deal for UK police is agreed between the Police Federation and the Home Office.

news.bbc.co.uk

Rooney hits double in England win

Wayne Rooney scores twice as England win 3-1 in Belarus to make it four wins from four World Cup qualifiers.

news.bbc.co.uk

Unemployment

How bad will things get in the jobs market?

news.bbc.co.uk

Watchdog sorry for bank failings

The financial services watchdog apologises for failing to spot banking problems which led to the government bail-out.

news.bbc.co.uk

Madonna and Ritchie confirm split

Pop star Madonna and her film director husband Guy Ritchie are to divorce, their PR representatives confirm.

news.bbc.co.uk

The big chill

Icelanders save up their hate for unsuspecting Brits

news.bbc.co.uk

US rivals to spar in final debate

The US presidential hopefuls are to meet in New York for the final pre-election debate, with domestic issues the key focus.

news.bbc.co.uk

In pictures

Madonna, Guy and their memorable moments

news.bbc.co.uk

Inflation riddle

Why talk of inflation falling as data shows it rising?

news.bbc.co.uk

Man admits botched bomb attack

A Muslim convert pleads guilty to attempted murder in a failed suicide bomb attack on an Exeter restaurant in May.

news.bbc.co.uk

Anger over council cash funding

Council leaders fear services may be hit as local authorities in Wales face below-inflation cash settlements.

news.bbc.co.uk

Recession fears knock US shares

Wall Street shares plummet on fresh fears of a global recession despite moves to strengthen the financial system.

news.bbc.co.uk

'Bomb material purchase' on CCTV

A man accused of attempted car bombings at Glasgow airport and in London was captured on CCTV, a jury hears.

news.bbc.co.uk

Scientists discover ray of hope for the red squirrel

Some red squirrels have developed immunity to a deadly disease carried by grey squirrels, scientists find.

news.bbc.co.uk

Jobless rise highest for 17 years

The number of people out of work in the UK soared by 164,000 over the summer, increasing the jobless total to 1.79 million.

news.bbc.co.uk