Properties of Ordinal Numbers

Proof

According to the properties of transitive sets, all elements of the sets \(\alpha\cup\{\alpha\}\), \(\bigcup X\), \(\bigcap X\), are transitive sets. Following the definition of ordinal numbers thy must be themselves ordinal numbers.

References

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

Contribute to BoP:

add a new Open Problem  add

add a new Comment (Branch)  add