In mathematical logic, given models $M$ and $N$ in the same language $L$, a function

$f:M\backslash to\; N$

is called an elementary embedding if $f(M)$ is an elementary substructure of $N$ and $f$ is a model isomorphism between $M$ and $f(M)$.

Elementary embeddings are the most important maps in model theory. Elementary embeddings whose domain is V (the universe of set theory) play an important role in the theory of large cardinals (see also critical point).

Model theory

Rudimenta enigo