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arXiv · 2608.07780

Embeddings, ultrapowers and direct powers

Pedro Teixeira Yago
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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 $\mathcal{A}^I / \mathcal{U} \hookrightarrow \mathcal{A}^I$.

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Pedro Teixeira Yago. 2026-08-07. Embeddings, ultrapowers and direct powers. https://arxiv.org/abs/2608.07780

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