2 citations · 2 across the 4 of their papers we have counts for
8 papers
Scott Ranks of Classifications of the Admissibility Equivalence Relation
William Chan, Matthew Harrison-Trainor, Andrew Marks
Let be a recursive language. Let be the set of -structures with domain . Let be a funct…
Finitely Generated Groups Are Universal
Matthew Harrison-Trainor, Meng-Che Ho
Universality has been an important concept in computable structure theory. A class of structures is universal if, informally, for any structure, of any kind, there is…
There is no classification of the decidably presentable structures
Matthew Harrison-Trainor
A computable structure is decidable if, given a formula of elementary first-order logic, and a tuple , we have a decision proced…
A first-order theory of Ulm type
Matthew Harrison-Trainor
The class of abelian -groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory whose models a…
On optimal Scott sentences of finitely generated algebraic structures
Matthew Harrison-Trainor, Meng-Che Ho
Scott showed that for every countable structure , there is a sentence of the infinitary logic , called a Scott sentence for , whose mo…
Some new computable structures of high rank
Matthew Harrison-Trainor, Gregory Igusa, Julia F. Knight
We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank , the computable infinitary theory is $\al…