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Welcome to the Cantor's Attic community. We aim to provide a comprehensive high-quality reference for all concepts of infinity in mathematics, including particularly the diverse large cardinal concepts, proof-theoretic ordinals, fine-structural ordinals and all other infinitary concepts studied in set theory, logic and mathematics.

How to help

This project aims to harness the abilities and efforts of the expert mathematical logic community---please help out! If you see a page that could be improved, please click to create an account, log in and make it better. We welcome edits to improve any of our pages by knowledgeable contributors. We especially welcome contributions of knowledgeable experts in mathematical logic. We welcome helpful edits by interested parties. Please follow our style guidelines.

Cantor's Attic style guidelines

Knowledgeable users should create new entries where they are needed

New entries should be written in a clear, elegant style, with all mathematical details correct.

  • Write in clear plain language.
  • Avoid excessive mathematical formalism. Use detailed mathematical notation only when this is necessary to illuminate the mathematical idea.
  • For grammar and punctuation, follow the Chicago Manual of Style.

The goal is to have an insightful and correct mathematical account of the concept, an informative summary essay that highlights the major facts about that concept and indicates where one may find further information. Comparative information about how the infinitary concept relates to others is especially valuable, and should be supported with citations. Please group closely related large cardinal concepts in sections on one page, as on the inaccessible cardinal page. (If the sections become large, we may consider breaking them off into their own pages.) We will build a database of outright implications and consistency strength implications (as well as other kinds of implications, such as inner model consistency or forcing extension consistency), which will be used to present the large cardinal and other hierarchies in clickable graphical form.

Some technical details

  • See the Help:Editing page.
  • When creating new pages, use a title that creates a very simple and relevant url. In particular, don't use accents or tex code in the url; write out greek letters, such as omega; don't include articles such as "the" in the url or the word "cardinal". Meanwhile, the displayed title for the post can be modified using {{DISPLAYTITLE: My great title}}, where of course it is fine to use tex, articles and the word "cardinal".
  • When creating links, use tex code in the link text as follows: [[actual page name | link $\tex$ text]], so that the tex code is displayed as the link text. Use the format [[main page#section title | link text]] to link to a section within a page.

Use references and citations to the professional literature

Please use citations and references liberally. The best references will have clickable links to on-line versions of them, such as the arxiv or doi. Use bibtex references in the style of the other pages. We will periodically collect references to the Library. Add suitable references and citations to other posts. Our bibtex system is still under construction. (We need better instructions here, with an example.)

Be respectful of other's contributions

This is a professional forum. Please use the discussion/talk pages before making major changes to someone else's contribution. Be considerate and polite, respectful of other's contribution efforts.

Projects needing help

Here is a list of tasks that need doing. Please update with subentries as appropriate.

  • Populate most of the cardinal entries with mathematical information
    • Add missing cardinal concepts to the main attic lists
    • Create those pages and add information
    • Improve the existing stub pages with additional or better information
    • Add references to existing pages to support the claims being made
  • Develop pages with background set-theoretic information
  • Figure out how to generate an RSS feed of new posts
    • It would be great to have an RSS feed of new posts that could be used in people's blogs
  • Major projects for graphical representation of the data
    • Develop a graphical representation of the implication and consistency strength relations between large cardinals (like a grand clickable version of the diagram in Kanamori's book) Such a diagram could be the main list on the upper attic page.
    • A smaller or condensed perhaps linear version of the same diagram in a widget graphical representation to appear automatically in each page, indicating visually roughly where that cardinal sits in the hierarchy. I can imagine something like a vertical sidebar version of the toolbar on many operating systems, where the currently relevant entry appears larger than the rest, as one moves around.