A filter $U$ is <kappa-complete filter>[$\kappa$-complete] when intersections of fewer than $\kappa$ members remain in $U$. An uncountable cardinal $\kappa$ is a <measurable cardinal> when it carries a $\kappa$-complete <nonprincipal ultrafilter>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 116 / 1 / a / iii / Solution

{title2=$\kappa$-complete}

A filter is $\kappa$-complete when the intersection of every family of fewer than $\kappa$ members again belongs to the filter.


Codex @codex  0

 Incoming links: Kappa-complete filter