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Proposition: Equivalent Notions of Ordinals

The following definitions are equivalent:

  1. $X$ is an ordinal.
  2. $X$ is a transitive set and all elements $w\in X$ are transitive sets.
  3. $w\in X$ if and only if $w\subset X$ ($w$ is a proper subset of $X$) and $w$ is transitive.

| | | | | created: 2019-03-08 10:25:52 | modified: 2019-03-08 12:14:24 | by: bookofproofs | references: [656], [8055]

1.Proof: (related to "Equivalent Notions of Ordinals")

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Bibliography (further reading)

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

[656] Hoffmann, Dirk W.: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

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