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math.LO2026
Structural vs. computational complexity
Johanna N. Y. Franklin, Dino Rossegger, Dan Turetsky
We consider highness in the context of computable structure theory and, particularly, the Scott rank of a structure. We define highness for Scott rank and highness for computably d…
math.LO2026
Scott Analysis below the Vaught Ordinal
David Gonzalez, Dino Rossegger, Dan Turetsky
We develop new tools for determining the existence of models of specific Scott ranks under countability conditions. Using these, we improve a result of Sacks by showing that any co…