Definable choice in nonstandard models

Construct a definable choice function selecting an element from each M-finite set A_s intersecting a fixed Pi-n subset X in a model of RCA-zero plus B-Sigma-n plus not-I-Sigma-n.

Background

The problem is posed in a nonstandard model with pairwise disjoint finite sets meeting a definable set X. It asks whether the stipulated intersections admit a definable uniform selection.

References

Is there a definable in $M$ choice function $f$ of $\langle A_s\rangle$, i.e., $f(s) \in A_s \cap X$?

— Open Problems in Mathematical Logic  (2608.26628 - Barmpalias et al., 27 Aug 2026) in 2025 Section 9