On the Decidability of the Σ2 Theories of the Arithmetic and Hyperarithmetic Degrees as Uppersemilattices. - James S. Barnes (J. Symb. Log., 2017)

Theorems of Hyperarithmetic Analysis and Almost theorems of Hyperarithmetic Analysis. - James S. Barnes; Jun Le Goh; Richard A. Shore (Bull. Symb. Log., 2022)

Halin's infinite ray theorems: Complexity and reverse mathematics. - James S. Barnes; Jun Le Goh; Richard A. Shore (J. Math. Log., 2025)