The following two definitions are due to [Andrzej Mostowski][mo] (1913 - 1975) and play a prominent role in the theory of ordinal numbers:


Definition: Mostowski Function and Collapse

Let $V$ be a set and $U$ be a universal set let $R$ be a well-founded relation defined on it. A function $\pi:V\to U$ defined recursively by $$\pi(x):=\{\pi(y)\mid y\in V\wedge yRx\}$$ is called the Mostowski function of $R.$ Its image $p[V]$ is called the Mostowski collapse of $R.$

Examples: 1 2 Motivations: 1 2

  1. Theorem: Mostowski's Theorem

Examples: 1 2
Motivations: 3 4
Proofs: 5 6
Theorems: 7

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  1. Hoffmann, D.: "Forcing, Eine Einführung in die Mathematik der Unabhängigkeitsbeweise", Hoffmann, D., 2018