Answer by Asaf Karagila for singular cardinals of every regular cofinality
Indeed as you thought $\aleph_{\kappa+\kappa}$ is a good candidate. The missed up point on the regularity of $\kappa$ comes in the fact that $\mathrm{cf}(\mu)$ is a regular cardinal for every...
View ArticleAnswer by Brian M. Scott for singular cardinals of every regular cofinality
Corrected: Suppose that there is some $\lambda<\kappa$ and a function $g:\lambda\to\aleph_{\kappa+\kappa}$ such that $\sup\{g(\xi):\xi\in\lambda\}=\aleph_{\kappa+\kappa}$. For each $\xi\in\lambda$...
View Articlesingular cardinals of every regular cofinality
First of all a couple of definitions which might be different to the standard ones:A function is called cofinal if $$f:\alpha\mapsto \beta$$is such that $$\sup\{...
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