Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Definition 4.7.1.19. Let $\alpha $ and $\beta $ be ordinals, given by the order types of well-ordered sets $(S, \leq )$ and $(T, \leq )$. We write $\alpha \leq \beta $ if there exists an initial segment embedding from $(S, \leq )$ to $(T, \leq )$ (note that this condition depends only on the order types of $S$ and $T$).