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It turns out that the occurence of forbidden self-contained sets is only a technical problem and we can circumvent it by skillfully defining a contained relation, as follows:

Definition: Contained Relation $"\in_X"$

Let $X$ be a set. The contained relation $\in_X\subseteq X \times X$ is a relation defined by $$\in_X:=\{(a,b)\in X\times X\mid a\in b\}.$$

| | | | | created: 2019-02-03 14:07:49 | modified: 2020-03-28 18:55:49 | by: bookofproofs | references: [8055]

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Bibliography (further reading)

[8055] Hoffmann, D.: “Forcing, Eine Einführung in die Mathematik der Unabhängigkeitsbeweise”, Hoffmann, D., 2018