# Seed

From Cantor's Attic

If $j:V \to M$ is an elementary embedding and $a \in j(D)$ for some set $D$, then $a$ is a *seed* for the measure $\mu$ on $D$ defined by $X \in \mu \iff X \subseteq D$ and $a \in j(X)$. In this case, we say that $a$ *generates* $\mu$ via $j$. If $b=j(f)(a)$ for some function $f \in V$, then we say that $a$ *generates* $b$ via the embedding. If every element of $M$ is generated by $a$, then we will say that $a$ generates all of $M$ or all of the embedding $j$.

This definition comes from Joel Hamkin's book "Forcing and Large Cardinals"