Corollary 2

— Let R be an algebraically closed field of infinite transcendence degree over its prime subfield. Then every field of the same characteristic as $\Omega$ is the ascending directed union of fields isomorphic to subfields of R.

For each field is the ascending directed union of finitely generated subfields over its prime field, and now it is enough to apply Cor. 1. \* Example. — This applies particularly in characteristic 0 in taking $\Omega = \mathbf{C}$ (« Lefschetz' principle »). \*