Embeddings, ultrapowers and direct powers

Abstract

We study when embeddings lift from structures to their ultrapowers, and when an ultrapower embeds into its direct power. We offer a refinement of Blass's theorem on the Rudin-Keisler order and introduce cardinal invariants ${\tau }_{\mathcal{A}}$ which imply the embeddability ${\mathcal{A}}^I/\mathcal{U}\hookrightarrow {\mathcal{A}}^I$.

12 pages