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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. $X$ is a transitive set and all elements $w\in X$ are transitive sets.

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1
Proofs: 2 3 4
Propositions: 5

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References

Bibliography

1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
2. Hoffmann, D.: "Forcing, Eine Einführung in die Mathematik der Unabhängigkeitsbeweise", Hoffmann, D., 2018