= Consistency strength of a worldly cardinal
Let $T=\mathrm{ZFC}+\text{“there is a worldly cardinal”}$ and $T^*=\mathrm{ZFC}+\operatorname{Con}(\mathrm{ZFC})$. A worldly $\kappa$ makes $V_\kappa$ a model of ZFC, and <arithmetic absoluteness for a rank-initial model> makes it a model of $T^*$, so $T$ proves $\operatorname{Con}(T^*)$. If $T^*$ proved $\operatorname{Con}(T)$, then the stronger theory $T$ would prove its own consistency, contradicting the <Gödel second incompleteness theorem>. Thus, assuming consistency, $T^*<_{\mathrm{Cons}}T$.
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