“Although the arguments here show that $KM$ is strictly stronger than $ZFC$ in consistency strength, it is not really very much stronger…”, especially that “if $\kappa$ is an inaccessible cardinal, then it is not difficult to argue in $ZFC$ that $$ is a model of $KM$”. If one assumes $\kappa$ is the least inaccessible cardinal so that $V_{\kappa}$ is a model of ZFC$ + “There is no inaccessible cardinal.” then by the usual understanding of $V_{|kappa+ 1}$ (i.e. $V_{\kappa +1}$ = $Powerset$($V_{\kappa}$) since one is arguing in $ZFC$), both $\kappa$ and $V_{\kappa}$ are sets in $V_{\kappa + 1}$ and the model of $KM$ in question is not merely a model of $KM$ but is a model of $KM$ + “There is a proper class of inaccessible cardinals” (at least). Am I correctly understanding the state of affairs and if not, would you please point out the errors in my under standing? Thanks. By the way, it is a very interesting blogpost.

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