It is proved in this paper that the positive abstraction scheme is consistent with extensionality only if one drops equality out of the language. The theory obtained is then compared with GPK, a well-known set theory based on an extended positive comprehension scheme.
"Positive abstraction and extensionality." J. Symbolic Logic 68 (3) 828 - 836, September 2003. https://doi.org/10.2178/jsl/1058448441