Burali–Forti paradox: Difference between revisions

The '''Burali–Forti paradox''' refers to the theorem that there is no set containing all [[von Neumann ordinal]]s. Essentially, if there were such a set, then it would itself be a von Neumann ordinal, contradicting [[wellthe axiom of foundation, which implies no set can be an element of itself. In second-foundedness]]order (ortheories moresuch directlyas Morse-Kelley set theory, this issue is circumvented by making the [[axiomcollection of regularity]]ordinals a proper class, while all ordinals are sets (and proper classes can not contain other proper classes).