The following two definitions are due to [Andrzej Mostowski][mo] (1913 - 1975) and play a prominent role in the theory of ordinal numbers:
[mo][https://mathshistory.st-andrews.ac.uk/Biographies/Mostowski/]
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
Examples: 1 2
Motivations: 3 4
Proofs: 5 6
Theorems: 7