Model theory and set theory
We show a sufficient condition guaranteeing that an elementary theory of a generic omega-stable structure (in an arbitrary relational language) obtained by the Hrushovski's construction (ab initio) does not admit elimination of imaginaries. In particular, we prove that strongly minimal sets, which refute the Zilber's conjecture, do not admit elimination of imaginaries, as well as almost strnogly minimal projective plane by J. Baldwin.
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