Corollary: Properties of Transitive Sets

(related to Definition: Transitive Set)

  1. If \(X\) is a transitive set, so is:

    1. the set \(X\cup\{X\}\), and
    2. the power set \(\mathcal P(X)\).
  2. If \(X\) is a set of transitive sets, so is:

    1. the union of its elements \(\bigcup X\), and
    2. the intersection of its elements \(\bigcap X\).

Proofs: 1

Motivations: 1
Proofs: 2 3

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  1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011