◀ ▲ ▶Branches / Settheory / Corollary: Strictly, Wellordered Sets and Transitive Sets
Corollary: Strictly, Wellordered Sets and Transitive Sets
(related to Theorem: Mostowski's Theorem)
For every strictlyordered set $(V,\prec),$ which is a wellorder, there is a unique transitive set $(X,\in_X)$ with the following properties:
 $(X,\in_X)$ is also a strictlyordered and wellordered set with respect to the contained relation $\in_X$
 Between the two orders $(V,\prec)$ and $(X,\in_X)$ there is an order embedding $\pi:V\to X,$ i.e. an injective function $\pi$ fulfilling the property $u\prec v\Longleftrightarrow \pi(u)\in_X\pi(v).$
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Hoffmann, D.: "Forcing, Eine EinfÃ¼hrung in die Mathematik der UnabhÃ¤ngigkeitsbeweise", Hoffmann, D., 2018