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Proposition: Equivalent Notions of Ordinals
The following definitions are equivalent:
- $X$ is an ordinal.
- $X$ is a transitive set and all elements $w\in X$ are transitive sets.
- $X$ 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
- Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
- Hoffmann, D.: "Forcing, Eine Einführung in die Mathematik der Unabhängigkeitsbeweise", Hoffmann, D., 2018