Let "$@_{\sf T}$" denote the first cardinal $\kappa$ such that $V_\kappa \models \sf T$.
This I describe as the first worldly cardinal with respect to $\sf T$.
Now, working in $\sf ZFC + @_{\sf ZFC + \exists \alpha. \operatorname {icc}(\alpha)} \text { exists}$:
Is $@_{\sf ZFC+ \exists \alpha.\operatorname { icc}(\alpha)} $ singular?
where $\operatorname {icc}$ stands for "strongly inaccessible".