If my understanding is correct, naive set theory needs to be restricted in order to avoid paradoxes including the Russell paradox. Typically, the restriction is expressed in terms of size. For example, the set of all sets must be excluded.
I recall that I came across a paper in Arxiv some time ago which explained that a useful restriction may be expressed in terms of symmetry conditions rather than size. Can anyone explain to me the concept and/or provide a link to the paper in question?