4 papers
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…
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…
Characterising SJT reducibility
Noam Greenberg, Andre Nies, Dan Turetsky
SJT reducibility between sets is defined by if for each computable function that is unbounded and nondecreasing, there is an -bound…
Topology, forcing, and graph colourings
Noam Greenberg, Dominique Lecomte, Dan Turetsky +1
We introduce a family of forcing notions that are helpful in showing that certain graphs do not have countable colourings of (additive) Borel class alpha. We construct graphs that…