Club reflection below an inaccessible cardinal
= Club reflection below an inaccessible cardinal
For inaccessible $\kappa$ and any predicate $R\subseteq V_\kappa$, the ordinals $\alpha<\kappa$ with $\langle V_\alpha,\in,R\cap V_\alpha\rangle\prec\langle V_\kappa,\in,R\rangle$ form a club. Closure under ranks of existential witnesses gives unboundedness, and the <elementary chain theorem> gives closedness.