nLab
strongly compact cardinal

Definition

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.

Properties

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.

References

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

For a basic theory, see

  • Thomas Jech?, Set theory.

Created on June 11, 2020 at 02:01:54. See the history of this page for a list of all contributions to it.