A proof of Hechler's theorem on embedding $\aleph_1$-directed sets cofinally into $(\omega^\omega,<^*)$

Abstract.

We give a proof of Hechler's theorem that any $\aleph_1$-directed partial order can be embedded via a ccc forcing notion cofinally into $\omega^\omega$ ordered by eventual dominance. The proof relies on the standard forcing relation rather than the variant introduced by Hechler.