AbstractIn positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+interprets the Kelley Morse class theory. Here we prove that GPK∞++ ACWF(ACWFbeing a form of the axiom of choice allowing to choose elements in well‐founded sets) and the Kelley‐Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞++ ACWFis a “strong” theory since “On is ramifiable” implies the existence of a proper clas