I raised the following question as part of another MO question, but I am following the suggestion of Nate Eldredge to make it a question in its own right.

For many years, there has a been a valuable web resource, hosted by Purdue, on the Consequences of the Axiom of Choice. Unfortunately, the page is no longer functioning, as you will quickly discover if you try submitting a form number. The URLs have changed. I suspect that Purdue redesigned its website at some point, changing the URLs, and that since Herman Rubin died a couple of years ago, there is now nobody responsible for maintaining the Axiom of Choice page. I tried emailing a couple of random people in the Purdue mathematics department to find out if something could be done to revive the page, but have received no response.

I am wondering if there is a way to revive this resource, ideally in a way that will prevent it from suffering a similar extinction risk a few years down the line. Perhaps some people can turn the page into a wiki, much in the way the OEIS evolved from a personal project of Neil Sloane's into a wiki? Also, maybe someone reading this knows more than I do about the situation at Purdue and can comment on what would be involved in making the data publicly available again.

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    $\begingroup$ A related post on Mathematics: What is current status of Consequences of the Axiom of Choice website? BTW since here we deal with various implications, perhaps a more suitable some kind of database - similar to pi-base or DaRT - could be more suitable format than a wiki. $\endgroup$ – Martin Sleziak Oct 10 '20 at 16:36
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    $\begingroup$ (Re-posted thanks to @‍MartinSleziak's spotting a typo.) @MartinSleziak, or the Lie-groups atlas? Although Groupprops shows that a Wiki database can be done well. \\ I also sent a mail to a colleague at Purdue to see if he has any thoughts. $\endgroup$ – LSpice Oct 10 '20 at 17:02
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    $\begingroup$ My colleague suggested e-mailing the computer-systems staff at Purdue, which I have now done. $\endgroup$ – LSpice Oct 10 '20 at 17:30
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    $\begingroup$ That's interesting, I hadn't been aware of that page. I'm a random person in the Purdue math department. However, this not an official response. @LSpice I sort of doubt the computer people will act on their own. Currently, I don't believe we have an official policy of what to do when the original owner of a webpage passes away. It seems a like a subtle question. $\endgroup$ – Donu Arapura Oct 10 '20 at 17:37
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    $\begingroup$ Looking at some old pages in the Wayback Machine, I see that some old versions of various files accompanying the book can be found. For example, the file models.dat. But I am pretty sure that people who worked on the new version mentioned in Asaf Karagila's answer have more recent data than we might be able find in some old Wayback Machine snapshot. $\endgroup$ – Martin Sleziak Oct 10 '20 at 17:40

Sorry I just saw this, and thank you @martin-sleziak for informing me of this question!

I'm still investigating what went wrong, but cgraph is back online:


About the original "Consequences of the axiom of choice" website I know Paul Howard was working on a new version (hopefully with cgraph integration), I will try to find out what is the status and post here again. Either way, please feel free to use cgraph, either from the website or by installing the program locally.

Let me know if you need any help, want to offer any help, or you discover any problems either per email or by opening an issue at either repository:

By the way, I have pledged to maintain cgraph for life, and I am open to suggestions to integrate it with or expand it for any wikis anyone wants to create. Just drop me a line!


Ioanna Dimitriou worked with Paul Howard at some point to create Jeffrey (also here). It used to have a working website, but now it's also not great.

One can install the software locally, or at the very least, one can open the source files on the website and search through them.

Hopefully she'll find a way to make the site operational again for the benefit of set theorists all over the world. And while it is certainly far from a Wiki level, it is at least a good start.


Paul Howard is a colleague of mine here at EMU. Several years ago I asked him if I could try to put his book into an online format (with a database underneath and Ruby on Rails on top).

My progress has stalled on the last 2 years, but you can see what we were able to do at

In response to comments below:

The links at the top of the page correspond to different aspects of Paul's book.

In order, the

  • articles, authors, journals, books, and excerpts links give information about every one of them listed in the book. if you click on the authors link, for example, you'll see every author listed in the book. click on an author, you'll see information about papers by that author that were cited in the book
  • forms link: goes to a page that lists every equivalence class of forms of the axiom of choice. if you click on a specific form, you'll see basic information about that equivalence class.
  • models link: goes to a page that has information about each of the models of set theory; click on one of the models, and you'll see, for example, a list of all the forms of the axiom of choice that are known to be true in that model, (each with its own link), a list of all the forms of the axiom of choice that are known to be false in that model), along with a lot more information.
  • notes link: Paul and Jean included a lot of little independent proofs of things that they did not find in the literature. This link lists all of the notes, and clicking on any note takes you to the statement and proof
  • implications link: Paul and Jean classified the different implications by 6 different types; this page lists all of the implications by type. Each type of implications has its own page; going to that page, and click on an implication, and you'll see information about the forms involved and how that implication was derived
  • tools: this was something that Paul had on his site that I reproduced here. You can put in versions of the axiom of choice by number and make little implication arrays, etc.

I hope this helps; I apologize for the length.


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