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nLab > Latest Changes: ZFA

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    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeNov 16th 2012
    • (edited Nov 16th 2012)

    Created ZFA, about ZF with atoms. I’ve added it to the foundations side bar under material set theories and a stack of links.

    • CommentRowNumber2.
    • CommentAuthorDexter Chua
    • CommentTimeJul 14th 2016

    Added description about the two possible types of atoms. The section on the category-theoretic approach should probably be moved to a separate page, since it is about Fraenkel-Mostowski models in particular, and not so much about ZFA itself.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJul 14th 2016

    Calling reflexive sets “atoms” seems to me to be a contradiction in terms; aren’t atoms supposed to be things that aren’t sets?

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 15th 2016

    It would be good to have a separate, more detailed page on FM models, but an outline at ZFA is not out of place, to my mind, at least at present.

    • CommentRowNumber5.
    • CommentAuthorDexter Chua
    • CommentTimeJul 15th 2016

    Calling reflexive sets “atoms” seems to me to be a contradiction in terms; aren’t atoms supposed to be things that aren’t sets?

    I agree that the first thing that comes to mind when someone mentions “atoms” would be “empty” atoms, but I guess reflexive/Quine atoms do play the role of atoms in ZFA, and it appears to be standard to call them Quine atoms. I have carefully worded the idea sections to say atoms are not made up of other sets, rather than having no elements.

    It would be good to have a separate, more detailed page on FM models, but an outline at ZFA is not out of place, to my mind, at least at present.

    Yes I agree. My main objection was that it appeared to claim it is a category-theoretic approach to ZFA, while it is actually a category-theoretic approach to FM models, and this distinction was not made clear in the paragraph as well.

    • CommentRowNumber6.
    • CommentAuthorDexter Chua
    • CommentTimeJul 15th 2016

    I’ve created a new page for FM models, and moved the relevant content there. A small paragraph was added to the ZFA page to mention FM models.

    • CommentRowNumber7.
    • CommentAuthorDexter Chua
    • CommentTimeJul 16th 2016

    Expanded a bit on empty atoms.

    • CommentRowNumber8.
    • CommentAuthorGuest
    • CommentTimeMay 31st 2020
    Surely the should be ZFU and you should call them urelements or urelemente. After all that's what the material set theorists call these theories.

    Roger Witte
    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 31st 2020
    • (edited May 31st 2020)

    Wikipedia says ZFA, and I’ve seen similar before. That seems to be what is accepted in English.

    Or course ur-elements or urelemente should be mentioned in the article. (Edit: And, they are.)

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 1st 2020

    ZFU is how I know this theory. I’ve added in parentheses:

    …called atoms or urelements (hence the alternative name ZFU)…

    diff, v8, current

    • CommentRowNumber11.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 2nd 2020

    Jech’s Set Theory (and the Springer LNM precursor) uses ’ZFA’, and that’s a pretty standard reference.

    • CommentRowNumber12.
    • CommentAuthorRichard Williamson
    • CommentTimeJun 3rd 2020
    • (edited Jun 3rd 2020)

    [Administrative note: merged two threads so that the discussion page has the historical discussion.]

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