On the regular extension axiom and its variants

Abstract

Abstract The regular extension axiom, REA, was first considered by Peter Aczel in the context of Constructive Zermelo‐Fraenkel Set Theory as an axiom that ensures the existence of many inductively defined sets. REA has several natural variants. In this note we gather together metamathematical results about these variants from the point of view of both classical and constructive set theory.