Subsystems of  with very low complexity comprehension studied in that framework have a language that does not merely express arithmetical sets, while all sets of naturals particular such theories prove to exist are just computable sets. Theorems therein can be a relevant reference point for weak set theories with a set of naturals, predicative separation and only some further restricted form of induction. Constructive reverse mathematics exists as a field but is less developed than its classical counterpart.
Subsystems of  that consider low complexity comprehension have a language beyond mere arithmetic representation; all natural number sets within these systems are computable. The theorems in this context can be relevant for weak set theories with natural numbers, predicative separation, and restricted induction. Constructive reverse mathematics is a related but less developed field.