Generic I0 at $\aleph_ω$

英文摘要：

In this paper it is introduced a generic large cardinal akin to I0, and its consequences are analyzed in the case that $\aleph_ω$ is such a generic large cardinal. In this case $\aleph_ω$ is Jónsson, and in a choiceless inner model many properties hold that are in contrast with PCF in ZFC.