Strongly compact cardinals

While I was creating the publication entry for the recent submitted preprint joint with A. W. Apter and T. Usuba, I decided it is worth writing a separate blogpost explaining how our results extend an ongoing problem in set theory, the violation of GCH at large cardinals from optimal assumptions.

In this blog post I will travel back to the 70s and discuss about a result that appeared here. Briefly, the result says that we can always find fast functions for strongly compact cardinals which are limits of strongly compact cardinals, without the need to force one.