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Canonical static concept record
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The collection of every ordinal, ordered by membership.
If were a set, it would itself determine an ordinal larger than every ordinal, giving the Burali–Forti contradiction.
wp-ordinalsep-set-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The ordinals form a proper class rather than a set.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-ordinalsep-set-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
For every ordinal , its successor is a strictly larger ordinal; therefore the ordinal hierarchy has no greatest member.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-ordinalopenlogic-set-theoryEach relation below starts at this concept.
No direct relations are authored in this direction.