be a particular set theory, for example the ZFC axioms and let T (possibly the same as S) also be a theory in L.

If M is a model for S, and N is an ''L''-structure such that

# N is a substructure of M, i.e. the interpretation of in N is
# N is a model of T
# the domain of N is a transitive class of M
# N contains all ordinals in Mthen we say

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