14 citations · 48 across the 31 of their papers we have counts for
51 papers
Recovering a structure from its tree of tuples
David Gonzalez, Matthew Harrison-Trainor, Julia Knight
We show that for each countable ordinal , there is a operator that, for all of Scott rank at most , takes copies of to copies of , where is…
On the Borel completeness of torsion-free abelian groups and a Slaman-Wehner degree spectrum
George Crittenden, Matthew Harrison-Trainor
It was recently shown by Paolini and Shelah, with another proof by Laskowski and Ulrich, that torsion-free abelian groups are Borel complete. This means that isomorphism for torsio…
Characterizing relative decidability in terms of model completeness
Matthew Harrison-Trainor, Liam Tan
A theory is said to be relatively decidable if for every model of , one can compute the elementary diagram of that model from its atomic diagram together with . We verify…
Scott spectral gaps for trees are bounded
Matthew Harrison-Trainor, J. Thomas Kim
Given a Borel class of trees, we show that there is a tree in that class whose Scott sentence is not too much more complicated than the definition of the class. In particular, if t…
Dichotomy results for classes of countable graphs
Vittorio Cipriani, Ekaterina Fokina, Matthew Harrison-Trainor +2
We study classes of countable graphs where every member does not contain a given finite graph as an induced subgraph -- denoted by for a given finite g…
Unfriendly jump inversions
Matthew Harrison-Trainor
We introduce a new technique in computable structure theory which we call unfriendly jump inversions. In contrast to the standard technique of jump inversions, we obtain the maxima…