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    AFA (Anti-Foundation Axiom) permits non-wellfounded sets — Carmelics
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    Supports→Under AFA, ℘* and ℘* are distinct

    AFA (Anti-Foundation Axiom) permits non-wellfounded sets

    Modality & PossibilityTruth & Knowledge
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    Under AFA, ℘* and ℘* are distinctUnder AFA, ℘* equals WF (well-founded sets only) while ℘* equals V (the full uni...

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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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