3 problems

Let $ba$ be a cardinal, and call $ba$ $ba$-compact when it has the $ba$-filter extension property: every $ba$-complete filter over $ba$ can be extended to a $ba$-complete ultrafilt…

A cardinal $\lambda$ is Fréchet when it carries a countably complete uniform ultrafilter, and it is isolated when it is Fréchet, is a limit cardinal, and is not a limit of Fréchet…

Let $\kappa$ be a cardinal. A cardinal is measurable if it carries a nonprincipal $\kappa$-complete ultrafilter, and $2^\kappa$ denotes the cardinality of its power set. UA continu…