The ${\Sigma }_2$ theory of ${\mathcal{D}}_h({\le }_h\mathcal{O})$ as an uppersemilattice with least and greatest element is decidable

James Barnes

We establish the decidability of the ${\Sigma }_2$ theory of ${\mathcal{D}}_h({\le }_h\mathcal{O})$, the hyperarithmetic degrees below Kleene's $\mathcal{O}$, in the language of uppersemilatt…