Let $(\alpha_\xi\mid\xi<\kappa)$ be a sequence such that $\{\alpha_\xi\mid\xi<\kappa\}=\alpha$. Find an increasing subsequence that has limit $\alpha$

score 156 · Answer 13 · 2026-03-26 06:29:15

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A question regarding Brian M. Scott's proof that $\text{cf}(\aleph_{\omega_1})=\omega_1$

Published on 26 Mar 2026 - 6:29

score 234 · Answer 14 · 2018-12-28 02:04:16

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Let $\aleph_\alpha$ be a singular cardinal and $2^{\aleph_\xi}=\aleph_\beta$ for all $\xi<\alpha$. Then $2^{\aleph_\alpha}=\aleph_\beta$

Published on 28 Dec 2018 - 2:04

score 438 · Answer 15 · 2018-12-29 02:49:20

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Is every (possibly infinite) sum of cardinal numbers defined?

Published on 29 Dec 2018 - 2:49

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Let $(\alpha_\xi\mid\xi<\kappa)$ be a sequence such that $\{\alpha_\xi\mid\xi<\kappa\}=\alpha$. Find an increasing subsequence that has limit $\alpha$

A question regarding Brian M. Scott's proof that $\text{cf}(\aleph_{\omega_1})=\omega_1$

Let $\aleph_\alpha$ be a singular cardinal and $2^{\aleph_\xi}=\aleph_\beta$ for all $\xi<\alpha$. Then $2^{\aleph_\alpha}=\aleph_\beta$

Is every (possibly infinite) sum of cardinal numbers defined?

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