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Nonuniformity of interpreting directed graphs in Friedman–Stanley linear-order embeddings
Noninterpretability conjecture. There do not exist $L_{\omega_1\omega}$ formulas that, for all directed graphs $G$ , define an interpretation of $G$ in $\Phi(G)$ .
Conjectureopencomputable-structure-theory infinitary-logic linear-orderingsarXiv posted 2 days ago

Nonuniformity of interpreting directed graphs in Friedman–Stanley linear-order embeddings