Comprehension Principle

The comprehension principle is the idea that given some property, there exists a unique set which exhaustively includes only objects which have that property.

This choice of axiom for establishing set theory leads to contradictions, such as Russel's paradox. As such, the comprehension principle is not used as an axiom in constructing Zermelo-Fraenkel set theory.

The analagous axiom within ZFC set theory is the axiom of comprehension, hence the name. This axiom restricts to subsets to prevent the problems with a general comprehension principle.