 The consistency-strength of FA is that of second-order arithmetic Z2 (i.e., real analysis), which is equal to that of Zermelo–Fraenkel set theory without the Axiom of Power Sets. The consistency-strength of first-order Peano arithmetic is much weaker, namely that of Zermelo–Fraenkel set theory without the Axiom of Power Sets and without the Axiom of Infinity. 