Short extenders forcings -- doing without preparations (Q2304539)

The study of the continuum function on singular cardinals poses a challenge since most results are independent of ZFC and depend on a combination of large cardinals and intricate forcing constructions. This article presents a new way to blow up the power set of a singular cardinal $\kappa$ to the successor of an arbitrary regular cardinal $\theta>\kappa$. The singular cardinal needs to be a limit of strong (up to some degree) cardinals and the forcing notion used is a variation of the short extender forcing found in [\textit{M. Gitik}, J. Math. Log. 12, No. 2, Article ID: 1250009, 113 p. (2012; Zbl 1271.03066)].