Meng-Che Ho

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math.LO2024

Scott analysis, linear orders and almost periodic functions

David Gonzalez, Matthew Harrison-Trainor, Meng-Che "Turbo" Ho

For any limit ordinal $λ$ , we construct a linear order $L_{λ}$ whose Scott complexity is $Σ_{λ + 1}$ . This completes the classification of the possible Scott sentence complexities of l…

math.LO2024

Torsion-free abelian groups of finite rank and fields of finite transcendence degree

Meng-Che "Turbo" Ho, Julia Knight, Russell Miller

Let $TFAb_{r}$ be the class of torsion-free abelian groups of rank $r$ , and let $FD_{r}$ be the class of fields of characteristic $0$ and transcendence de…

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.LO2024

Algorithmically finite, universal, and $*$ -universal groups

Uri Andrews, Meng-Che "Turbo" Ho

The study of the word problems of groups dates back to Dehn in 1911, and has been a central topic of study in both group theory and computability theory. As most naturally occurrin…

Scott analysis, linear orders and almost periodic functions

Torsion-free abelian groups of finite rank and fields of finite transcendence degree

Two results on complexities of decision problems of groups

Algorithmically finite, universal, and ∗-universal groups

Algorithmically finite, universal, and $*$ -universal groups