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nLab > Latest Changes: neutral non-well-founded set theory

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  1. starting page on the most general notion of set theories without the axiom of foundation and Mostowski’s principle

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2022

    The “important examples” mentioned would deserve more reference than just the mysterious symbols “ZF ↺ZF^{\circlearrowleft}” and “IBZ ↺IBZ^{\circlearrowleft}”.

    diff, v3, current

  3. Added reference

    • Paul Halmos, Naive Set Theory. Princeton, NJ: D. Van Nostrand Company, 1960.

    as it presents a set theory equivalent to ZFC ↺ZFC^{\circlearrowleft}.

    Anonymous

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2022
    • (edited Nov 28th 2022)

    You should you say what the notation “ZF ↺ZF^{\circlearrowleft}” and “IBZ ↺IBZ^{\circlearrowleft}” means.

    I guess you mean “ZF without foundation”, etc., but this ought to be said.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2022

    In lack of a reaction to #2 and #4, I went ahead and added (here) a comment:

    Here the superscript “↺\scriptsize{\circlearrowleft}” probably means “omit the axiom of foundation”, and “ZFZF” refers to Zermelo-Fraenkel set theory.

    diff, v5, current

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