Classes of Ulm type and coding rank-homogeneous trees in other structures

@article{Fokina2011ClassesOU,
  title={Classes of Ulm type and coding rank-homogeneous trees in other structures},
  author={Ekaterina B. Fokina and Julia F. Knight and Alexander G. Melnikov and Sara Quinn and C. Safranski},
  journal={J. Symb. Log.},
  year={2011},
  volume={76},
  pages={846-869}
}
The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of “rank-homogeneous” trees. We consider these conditions as a possible definition of what it means for a class of structures to have “Ulm type”. The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply this result to show that there is no Turing… CONTINUE READING