1. Www.axiomofchoice.com/ axiom of choice From MathWorldThe axiom of choice is related to the first of Hilbert s problems. In contexts sensitive to the axiom of choice, the notation ZF is often used to http://www.axiomofchoice.com/

2. The Axiom Of Choice Netherlands site with news, interviews, pictures, music samples, reviews, and links. http://www.cs.uu.nl/people/jur/progrock.html

3. 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

Next: The Axiom of Choice Up: Frequently Asked Questions in Mathematics Previous: Master Mind Axiom of Choice and Continuum Hypothesis The Axiom of Choice Cutting a sphere into pieces of larger volume The Continuum Hypothesis Alex Lopez-Ortiz Fri Feb 20 21:45:30 EST 1998

4. 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

Consequences of the Axiom of Choice Project Homepage The book Consequences of the Axiom of Choice by Paul Howard Send E-Mail to Paul Howard and Jean E. Rubin Send E- Mail to Jean Rubin is volume 59 in the series Mathematical Surveys and Monographs published by the American Mathematical Society in 1998. This book is a survey of research done during the last 100 years on the axiom of choice and its consequences. (Connect to The AMS Bookstore for ordering information.) The Consequences of the Axiom of Choice Project is a continuation of the research that produced the book. The authors would appreciate learning of any corrections or additions that should be made to the project. (phoward@emunix.emich.edu, jer@math.purdue.edu) To see the PDF version of a form enter its number below. The form number On this page you will find: Changes and additions to the data base that have occurred since publication of the book A TeX version of the implication table, Table 1 which may be downloaded and printed. (Hold down the shift key and click on the file name to download.) A TeX version of the auxillary table

5. Axiom Of Choice This page gives a brief explanation of the axiom of choice and links to other related websites. http://www.math.vanderbilt.edu/~schectex/ccc/choice.html

a home page for the AXIOM OF CHOICE an introduction and links collection by Eric Schechter , Vanderbilt University The Axiom of Choice ( AC ) was formulated about a century ago, and it was controversial for a few of decades after that; it may be considered the last great controversy of mathematics. It is now a basic assumption used in many parts of mathematics. In fact, assuming AC is equivalent to assuming any of these principles (and many others): Given any two sets, one set has cardinality less than or equal to that of the other set i.e., one set is in one-to-one correspondence with some subset of the other. ( Historical remark: It was questions like this that led to Zermelo 's formulation of AC.) Any vector space over a field F has a basis i.e., a maximal linearly independent subset over that field. ( Remark: If we only consider the case where F is the real line, we obtain a slightly weaker statement; it is not yet known whether this statement is also equivalent to AC.) Any product of compact topological spaces is compact. (This is now known as Tychonoff's Theorem , though Tychonoff himself only had in mind a much more specialized result that is not equivalent to the Axiom of Choice.)

6. 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

a home page for the AXIOM OF CHOICE an introduction and links collection by Eric Schechter , Vanderbilt University The Axiom of Choice ( AC ) was formulated about a century ago, and it was controversial for a few of decades after that; it may be considered the last great controversy of mathematics. It is now a basic assumption used in many parts of mathematics. In fact, assuming AC is equivalent to assuming any of these principles (and many others): Given any two sets, one set has cardinality less than or equal to that of the other set i.e., one set is in one-to-one correspondence with some subset of the other. ( Historical remark: It was questions like this that led to Zermelo 's formulation of AC.) Any vector space over a field F has a basis i.e., a maximal linearly independent subset over that field. ( Remark: If we only consider the case where F is the real line, we obtain a slightly weaker statement; it is not yet known whether this statement is also equivalent to AC.) Any product of compact topological spaces is compact. (This is now known as Tychonoff's Theorem , though Tychonoff himself only had in mind a much more specialized result that is not equivalent to the Axiom of Choice.)

7. Axiom Of Choice This page gives a brief explanation of the axiom of choice and links to other related websites. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Paul Howard's Web Page Eastern Michigan University axiom of choice. http://www.emunix.emich.edu/~phoward/

Paul Howard Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197 Information Phone: (734) 487-1294 Office: 516 E Pray-Harrold email: phoward@emunix.emich.edu Send email: Mail Other Sites Information on the "Consequences of the Axiom of Choice" Project can be found at CONSEQUENCES OF AC EMU Math Department Web Page EMU MATH Current Classes and Schedule Current schedule

9. The Axiom Of Choice Netherlands site with news, interviews, pictures, music samples, reviews, and links. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Zermelo's Axiom Of Choice -- From MathWorld Zermelo s axiom of choice. COMMENT On this Page. SEE axiom of choice. Pages Linking Here http://mathworld.wolfram.com/ZermelosAxiomofChoice.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Zermelo's Axiom of Choice SEE: Axiom of Choice [Pages Linking Here]

11. Axiom Of Choice - Official Site axiom of choice are musicians with their roots in traditional Persian music. Guitarist Loga Ramin Torkian and vocalist Mamak Khadem combine Eastern http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. New Foundations Home Page The following results are known NF disproves the axiom of choice (Specker, 1953). NF proves Infinity (corollary of the previous point). http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Sci.math FAQ: The Axiom Of Choice Subject sci.math FAQ The axiom of choice. This article was archived around 17 Feb 2000 225552 GMT. All FAQs in Directory scimath-faq http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/axiomchoice.html

Note from archiver cs.uu.nl: This page is part of a big collection of Usenet postings, archived here for your convenience. For matters concerning the content of this page , please contact its author(s); use the source , if all else fails. For matters concerning the archive as a whole, please refer to the archive description or contact the archiver. Subject: sci.math FAQ: The Axiom of Choice This article was archived around: 17 Feb 2000 22:55:52 GMT All FAQs in Directory: sci-math-faq All FAQs posted in: sci.math Source: Usenet Version Archive-name: sci-math-faq/axiomchoice Last-modified: February 20, 1998 Version: 7.5 http://www.jazzie.com/ii/math/index.html http://www.jazzie.com/ii/math/index.html Alex Lopez-Ortiz alopez-o@unb.ca http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick

14. [FOM] 195The Axiom Of Choice FOM 195The axiom of choice Harvey Friedman friedman at math.ohiostate.edu Mon Nov 3 131130 EST 2003 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Axiom Of Choice - Wikipedia, The Free Encyclopedia The axiom of choice is typically abbreviated AC, or C as a suffix. Until the late 19th century, the axiom of choice was often used implicitly. http://en.wikipedia.org/wiki/Axiom_of_choice

16. Rubin, Jean E. Purdue University Set theory, axiom of choice. http://www.math.purdue.edu/~jer/

Jean E. Rubin Professor of Mathematics Purdue University West Lafayette, IN 47907-1395 Information It is with deep regret that we must announce the passing of Professor Jean E. Rubin on Friday, October 25, 2002. Please click below for the web page of the book ``Consequences of the Axiom of Choice'' by Paul Howard and Jean E. Rubin. "CONSEQUENCES of AC" AC PROJECT Please be advised that the links following "Other Web points of interest" are not being maintained. Please refer to the official Math Department course web pages for the most current information using the following links: Math 165, Fall 2002 Other Web points of interest: MA 165 Webpage Fall 2002 MA 387 Webpage Fall 2002 MA 166 Webpage Spring 2002 Course Rosters ... ssociation of Symbolic Logic The ASL Business office e-mail: asl@math.uiuc.edu. West Lafayette Public Library Smitty's LSO Home Page West Lafayette City Hall ... Logic Program E-MAIL ADDRESSES for MathWorks (Makes MATLAB) support@mathworks.com - Technical support

17. FAQ Launcher Relevance Of The Axiom Of Choice Gateway to Relevance of the axiom of choice http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. TalkAxiom Of Choice - Wikipedia, The Free Encyclopedia Do Wikipedia articles assume the axiom of choice unless otherwise mentioned? From the article Jerry Bona once said The axiom of choice is obviously http://en.wikipedia.org/wiki/Talk:Axiom_of_choice

19. Jebara Infinite products of integers and the axiom of choice A restricted axiom of choice Brief history of the negation of the axiom of choice The story http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. Axiom Of Choice And Its Equivalents - Apronus.com axiom of choice (AC) If I Y are sets, AI Y and /\(x-I) A(x) != O then there exists a function fI- u(Y) such that /\(x-I) f(x)-A(x). http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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