Franklin's Notes

Transitive model

A transitive model of set theory (this could be of ZFC , or another theory of sets) is any model $\langle\mathrm{M},\in\rangle$ that is both standard and transitive. It is standard if the symbol $\in$ is interpreted as the standard membership relation in set theory, and it is transitive if the universe $\mathrm{M}$ is a transitive set, i.e. if $A\subset\mathrm{M}$ for all $A\in M$.



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