4 papers
Infinite Belligerent Jump Inversion and Computable Scott Analysis
Uri Andrews, David Gonzalez, Hongyu Zhu
Scott analysis provides two fundamental tools for studying countable structures: Scott sentences, which characterize structures up to isomorphism, and back-and-forth relations, whi…
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…
Classifying the complexity of models of arithmetic
David Gonzalez, Mateusz ÅeÅyk, Dino Rossegger +1
We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored line…
The Borel complexity of the class of models of first-order theories
Uri Andrews, David Gonzalez, Steffen Lempp +2
We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theori…