Transitive model

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.

Examples

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.

References

Jech, Thomas (2003). Set Theory. Springer Monographs in Mathematics (Third Millennium ed.). Berlin, New York: Springer-Verlag. ISBN 978-3-540-44085-7. Zbl 1007.03002.

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