Full Idea
The comprehension axiom says that any collection of objects that can be clearly specified can be considered to be a set.
Gist of Idea
Comprehension Axiom: if a collection is clearly specified, it is a set
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.2)
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.62
A Reaction
This is virtually tautological, since I presume that 'clearly specified' means pinning down exact which items are the members, which is what a set is (by extensionality). The naïve version is, of course, not so hot.