Definability over $\mathrm{B}\hat{I}{\pounds }_2^0$-models

Chi Tat Chong, Tin Lok Wong

Let $\mathfrak{M}=(M,\mathcal{X})$ be a model of $\mathsf{RCA}_0+\text{$Σ^0_2$-bounding}$ in which $\hat{I}{\pounds }_2^0(A)$-induction fails for some $A\in \mathcal{X}$. We show that (i) if $\mathf…