nLab strongly compact cardinal


A cardinal κ\kappa is strongly compact if any κ\kappa-complete filter can be extended to a κ\kappa-complete ultrafilter.

Here a filter is κ\kappa-complete if it is closed under intersections of families with fewer than κ\kappa elements.


Strongly compact cardinals are measurable cardinals.

The existence of a proper class of strongly compact cardinals implies that images of accessible functors are accessible as long as they are complete or cocomplete.


Strongly compact cardinals were introduced by Keisler and Tarski in 1963.

For a basic theory, see

Created on June 11, 2020 at 06:01:54. See the history of this page for a list of all contributions to it.