Matthew Harrison‐Trainor

most citedDegree Spectra of Relations on a Cone

2 citations · 2 across the 4 of their papers we have counts for

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math.LO2024

Back-and-forth equivalent group von Neumann algebras

Isaac Goldbring, Matthew Harrison-Trainor

We prove that if $G$ and $H$ are $α$ -back-and-forth equivalent groups (in the sense of computable structure theory) for some ordinal $α \geq ω$ , then their group von Neumann algebra…

math.LO2024

Two results on complexities of decision problems of groups

Uri Andrews, Matthew Harrison-Trainor, Meng-Che "Turbo" Ho

We answer two questions on the complexities of decision problems of groups, each related to a classical result. First, C. Miller characterized the complexity of the isomorphism pro…

math.LO2014★ 2 cited

Degree Spectra of Relations on a Cone

Matthew Harrison-Trainor

Let $A$ be a mathematical structure with an additional relation $R$ . We are interested in the degree spectrum of $R$ , either among computable copies of $A$ when…

math.LO2014

Independence in computable algebra

Matthew Harrison-Trainor, Alexander Melnikov, Antonio Montalbán

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply…