Notes on the Equiconsistency of ZFC Without the Power Set Axiom and Second-Order Arithmetic

We demonstrate that theories Z−, ZF−, ZFC− (minus means the absence of the Power Set axiom) and PA2, PA2− (minus means the absence of the Countable Choice schema) are equiconsistent to each other. The methods used include the interpretation of a power-less set theory in PA2− via well-founded trees, as well as the Gödel constructibility in said power-less set theory.