Proper class: Difference between revisions

Created page with "In second-order set theories, such as Morse-Kelley set theory, a proper class is a collection of objects which is too large to be a set - either because that would cause a paradox, or because it contains another proper class. The axiom of limitation of size implies that any two proper classes can be put in bijection, implying they all have "size \(\mathrm{Ord}\)". Russel's paradox combined with the axiom of regularity ensure that \(V\), the class of all sets, is a proper..."