Recovering a structure from its tree of tuples

David Gonzalez, Matthew Harrison-Trainor, Julia Knight

We show that for each countable ordinal $\alpha$, there is a ${\mathbf{\Delta }}_{\alpha }^0$ operator that, for all $A$ of Scott rank at most $\alpha$, takes copies of $T_A$ to copies of $A$, where $T_A$ is…