Transitive model

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In mathematical set theory, a transitive model is a model of set theory that is standard and transitive. Standard means that the membership relation is the usual one, and transitive means that the model is a transitive set or class.


  • An inner model is a transitive model containing all ordinals.
  • A countable transitive model (CTM) is, as the name suggests, a transitive model with a countable number of elements.