TITLE: Imaginaries in the Henson graph
QUESTION [1 upvotes]: Does the theory of the Henson graph has weak elimination of imaginaries?
The Henson graph is the countable homogeneous-universal triangle-free graph.

REPLY [1 votes]: Yes. In the paper An axiomatic approach to free amalgamation, Gabe Conant defined the class of free amalgamation theories and proved that every such theory has weak elimination of imaginaries (Theorem 5.6). The theory of the Henson graph is one of the main examples of a free amalgamation theory.
I'm not sure whether the special case of weak elimination of imaginaries for the Henson graph appeared in the literature before Gabe's paper. It wouldn't surprise me if it was folklore.
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