The Σ2 theory of Dh(⩽hO) as an uppersemilattice with least and greatest element is decidable
James Barnes · Computability · 2021
The decidability of the two quantifier theory of the hyperarithmetic degrees below Kleene’s [Formula: see text] in the language of uppersemilattices with least and greatest element is established. This requires a new kind of initial segment result and a new extension of embeddings result both in the hyperarithmetic setting.