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