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The hierarchy generated from the empty set by successor power sets and unions at limit stages; with the Foundation axiom, every set has a rank and occurs at some stage.
openlogic-set-theorysep-set-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Ordinals index the successor and limit stages of the cumulative hierarchy, allowing the rank of a set to be stated precisely.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
openlogic-set-theorysep-set-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The successor clause adds every subset of the preceding stage; limit stages instead take unions of all earlier stages.
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.
openlogic-set-theorysep-set-theoryEach relation below starts at this concept.
No direct relations are authored in this direction.