Every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in that structure.
Trace definability I: preservation and characterizations
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We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of it.
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Externally definable fsg groups in NIP theories
Every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in that structure.