3 papers
math.LO2023
Halin's Infinite Ray Theorems: Complexity and Reverse Mathematics: Version E
James S. Barnes, Jun Le Goh, Richard A. Shore
Halin [1965] proved that if a graph has many pairwise disjoint rays for each then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other…
math.LO2017
The theory of as an uppersemilattice with least and greatest element is decidable
James Barnes
We establish the decidability of the theory of , the hyperarithmetic degrees below Kleene's , in the language of uppersemilatt…
math.LO2016
On the decidability of the theories of the arithmetic and hyperarithmetic degrees as uppersemilattices
James Barnes
We establish the decidability of the theory of both the arithmetic and hyperarithmetic degrees in the language of uppersemilattices i.e. the language with and $\sqc…