Large cardinals and their effect on the continuum function on regular cardinals

Abstract

We will summarise some of the more and less known results on the generalisation of the Easton theorem in the context of large cardinals. In particular, we will consider inaccessible, Mahlo, weakly compact, Ramsey, measurable, strong, Woodin, and supercompact cardinals.

The paper concludes with a result from the opposite end of the spectrum: namely, how to kill all large cardinals in the universe.

Keywords

• Easton funtion
• large cardinals
• regular cardinals