Differential-Algebraic jet Spaces Preserve Internality to the Constants. - Zoé Chatzidakis; Matthew Harrison-Trainor; Rahim Moosa (J. Symb. Log., 2015)

Preferential Structures for Comparative Probabilistic Reasoning. - Matthew Harrison-Trainor; Wesley H. Holliday; Thomas F. Icard III (AAAI, 2017)

The Gamma question for many-one degrees. - Matthew Harrison-Trainor (Ann. Pure Appl. Log., 2017)

Degrees of Categoricity on a cone via η-Systems. - Barbara F. Csima; Matthew Harrison-Trainor (J. Symb. Log., 2017)

Computable Functors and Effective interpretability. - Matthew Harrison-Trainor; Alexander G. Melnikov; Russell G. Miller; Antonio Montalbán (J. Symb. Log., 2017)

Computable valued fields. - Matthew Harrison-Trainor (Arch. Math. Log., 2018)

The Complexity of Countable Structures. - Matthew Harrison-Trainor (Bull. Symb. Log., 2018)

There is no classification of the decidably presentable structures. - Matthew Harrison-Trainor (J. Math. Log., 2018)

Left-orderable Computable Groups. - Matthew Harrison-Trainor (J. Symb. Log., 2018)

Borel Functors and Infinitary Interpretations. - Matthew Harrison-Trainor; Russell G. Miller; Antonio Montalbán (J. Symb. Log., 2018)

Inferring probability comparisons. - Matthew Harrison-Trainor; Wesley H. Holliday; Thomas F. Icard III (Math. Soc. Sci., 2018)

A first-order theory of Ulm type. - Matthew Harrison-Trainor (Comput., 2019)

Effective aspects of algorithmically random structures. - Matthew Harrison-Trainor; Bakh Khoussainov; Daniel Turetsky (Comput., 2019)

Automatic and Polynomial-Time Algebraic Structures. - Nikolay Bazhenov 001; Matthew Harrison-Trainor; Iskander Sh. Kalimullin; Alexander G. Melnikov; Keng Meng Ng (J. Symb. Log., 2019)

First-order possibility Models and Finitary Completeness Proofs. - Matthew Harrison-Trainor (Rev. Symb. Log., 2019)

Degrees of categoricity above limit ordinals. - Barbara F. Csima; Michael Deveau; Matthew Harrison-Trainor; Mohammad Assem Mahmoud (Comput., 2020)

Graphs are not universal for online computability. - Rodney G. Downey; Matthew Harrison-Trainor; Iskander Sh. Kalimullin; Alexander G. Melnikov; Daniel Turetsky (J. Comput. Syst. Sci., 2020)

The Logic of Comparative Cardinality. - Yifeng Ding; Matthew Harrison-Trainor; Wesley H. Holliday (J. Symb. Log., 2020)

Computability of Polish Spaces up to Homeomorphism. - Matthew Harrison-Trainor; Alexander G. Melnikov; Keng Meng Ng (J. Symb. Log., 2020)

Non-density in punctual computability. - Noam Greenberg; Matthew Harrison-Trainor; Alexander G. Melnikov; Dan Turetsky (Ann. Pure Appl. Log., 2021)

Finitely generated groups are universal among finitely generated structures. - Matthew Harrison-Trainor; Meng-Che Turbo Ho (Ann. Pure Appl. Log., 2021)

The property "arithmetic-is-recursive" on a cone. - Uri Andrews; Matthew Harrison-Trainor; Noah Schweber (J. Math. Log., 2021)

Scott Complexity of Countable Structures. - Rachael Alvir; Noam Greenberg; Matthew Harrison-Trainor; Dan Turetsky (J. Symb. Log., 2021)

Some Questions of Uniformity in Algorithmic Randomness. - Laurent Bienvenu; Barbara F. Csima; Matthew Harrison-Trainor (J. Symb. Log., 2021)

An Introduction to the Scott Complexity of Countable Structures and a Survey of Recent Results. - Matthew Harrison-Trainor (Bull. Symb. Log., 2022)

Relationships between Computability-Theoretic Properties of Problems. - Rod Downey; Noam Greenberg; Matthew Harrison-Trainor; Ludovic Patey; Dan Turetsky (J. Symb. Log., 2022)

The Tree of Tuples of a Structure. - Matthew Harrison-Trainor; Antonio Montalbán (J. Symb. Log., 2022)

An analysis of random elections with large numbers of voters. - Matthew Harrison-Trainor (Math. Soc. Sci., 2022)

A Minimal Set Low for Speed. - Rod Downey; Matthew Harrison-Trainor (J. Symb. Log., 2022)

Coding information into all infinite subsets of a dense set. - Matthew Harrison-Trainor; Patrick Lutz (CoRR, 2023)

Which Classes of Structures Are Both Pseudo-Elementary and Definable by an Infinitary Sentence? - Will Boney; Barbara F. Csima; Nancy A. Day; Matthew Harrison-Trainor (Bull. Symb. Log., 2023)

Computable Stone spaces. - Nikolay Bazhenov 001; Matthew Harrison-Trainor; Alexander G. Melnikov (Ann. Pure Appl. Log., 2023)

Iterated Priority Arguments in Descriptive Set Theory. - Adam R. Day; Noam Greenberg; Matthew Harrison-Trainor; Dan Turetsky (Bull. Symb. Log., 2024)

Enumerations of families closed under finite differences. - Noam Greenberg; Matthew Harrison-Trainor; Joseph S. Miller; Dan Turetsky (Comput., 2024)

Computable learning of natural hypothesis classes. - Syed Akbari; Matthew Harrison-Trainor (COLT, 2025)

The logic of cardinality comparison without the axiom of choice. - Matthew Harrison-Trainor; Dhruv Kulshreshtha (Ann. Pure Appl. Log., 2025)

Two results on complexities of decision problems of groups. - Uri Andrews; Matthew Harrison-Trainor; Meng-Che Ho (Int. J. Algebra Comput., 2025)