User blog comment:DontDrinkH20/Some Explanations of Certain Large Cardinals/@comment-11227630-20181017041904/@comment-11227630-20181017161643

Ordinal \(\kappa\) is inaccessible iff \(\forall R\subseteq V_\kappa\exists\alpha<\kappa(\langle V_\alpha,\in,R\cap V_\alpha\rangle\prec\langle V_\kappa,\in,R\rangle)\) (not on Cantor's attic. It's showed in the book The Higher Infinite). Cancel the R we get a weaker \(\exists\alpha<\kappa(V_\alpha\prec V_\kappa)\), then \(\alpha\) is 0-extendible. So the 0-extendible is smaller than the inaccessible. But I'm not sure about the size of the 0-extendible in the scale of worldly cardinals.