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    Under AFA, ℘* equals WF (well-founded sets only) while ℘*... — Carmelics
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    Supports→Under AFA, ℘* and ℘* are distinct

    Under AFA, ℘* equals WF (well-founded sets only) while ℘* equals V (the full universe including non-wellfounded sets)

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    Related

    AFA (Anti-Foundation Axiom) permits non-wellfounded setsUnder AFA, ℘* and ℘* are distinct

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    V (the universe of all sets) is not a set

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    Related propositions within the same area of thought.
    81%
    AFA (Anti-Foundation Axiom) permits non-wellfounded sets81%
    Cantor's Theorem implies that no set can equal its own power set79%
    Nothing can be missing from V (the universe of all sets)79%

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    SEP: nonwellfounded-set-theory
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    Assuming FA, the fixed points are unique; frequently they are the empty set. With AFA, the greatest fixed points usually have non-wellfounded members. We shall study this in more detail when we turn to coalgebra. For now, we return to the last of the example equations at the top of this section, V   =  ℘V. This equation has no solutions in sets due to Cantor’s Theorem. However, in terms of classes, this equation does have solutions, as we know. The universal class V is a solution

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