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math.LO2022
Degrees of categoricity and treeable degrees
Barbara F. Csima, Dino Rossegger
We give a characterization of the strong degrees of categoricity of computable structures greater or equal to . They are precisely the \emph{treeable} degrees -- the l…
math.LO2022
The structural complexity of models of arithmetic
Antonio Montalbán, Dino Rossegger
We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than and that non-standard models of…
math.LO2022
Relations enumerable from positive information
Barbara F. Csima, Luke MacLean, Dino Rossegger
We study countable structures from the viewpoint of enumeration reducibility. Since enumeration reducibility is based on only positive information, in this setting it is natural to…