Consequences of the Axiom of Choice Project Homepage

It is with deep regret that we announce the death of Jean Rubin on October 25, 2002.

The book Consequences of the Axiom of Choice by Paul Howard ( Send E-Mail to Paul Howard ) and Jean E. 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. We would appreciate learning of any corrections or additions that should be made to the project. (phoward@emunix.emich.edu)

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, Table 2 which may be downloaded and printed (Hold down the shift key and click on the file name to download.)
• A view of the implication table, Table I, restricted to any subset of 30 or fewer forms of the axiom of choice. (Fill out the form below.)
  To see the implication table (Table I) restricted to a subset of the forms enter the form numbers (thirty forms maximum) separated by spaces or commas below.

  The list of form numbers
  

• A listing of all models known to satisfy any specified set of conditions. (Complete the form below.)
  To see a list of all models with specified characteristics:
  

  1. Enter the numbers of the forms that are to be true in the model separated by spaces or commas below. (Ten forms maximum)

     The list of forms to be TRUE in the model(s)
     

  2. Enter the numbers of the forms that are to be false in the model separated by spaces or commas below. (Ten forms maximum)

     The list of forms to be FALSE in the model(s)
     
• A .pdf file giving the text of any form.
  To see the PDF version of a form enter its number below.

  The form number
  

• A list of forms containing a single word or phrase
  Enter the word or phrase for which you want to search: