Embedding partially ordered sets into ωω

Abstract

We investigate some natural questions about the class of posets which can be embedded into 〈ωω, ≤*〉. Our main tool is a simple ccc forcing notion HE which generically embeds a given poset E into 〈ωω, ≤*〉 and does this in a "minimal" way (see Theorems 9.1, 10.1, 6.1 and 9.2).