= Coherent coinfinite injections into omega
{title2=$e_\alpha\upharpoonright\beta=^*e_\beta$}
There are <injections> $e_\alpha:\alpha\to\omega$ for $\alpha<\omega_1$, each with coinfinite range, with $e_\alpha\upharpoonright\beta$ equal to $e_\beta$ outside a <finite set>. At countable limits, extend partial <functions> along a cofinal sequence, repair finitely many collisions, and reserve a fresh omitted natural number at each step. The reserved sequence makes the union coinfinite and permits all later successor steps.
Back to article page
