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7. Model-theoretic equivalence relations


    1. Add remark

      Problem 7.1.

      Is there an $L_{\omega_1,\omega}$-elementary class $K$ of structures which is Borel complete and there is an $X\subseteq \omega$ such that there is no $X$-computable model in $K$ of Scott rank $\omega_1^X$?


        • Add remark

          Problem 7.2.

          Consider the equivalence relations on countable structures, by model theoretic bi-interpretability (in first-order logic). Is this equivalence relation $\Sigma^1_1$-complete? We may ask both the question of completeness as a set and question of completeness as an equivalence relations.

              Cite this as: AimPL: Invariant descriptive computability theory, available at http://aimpl.org/invdesccomp.