The 2 theory of Dh(≤h O) as an uppersemilattice with least and greatest element is decidable
Abstract
We establish the decidability of the 2 theory of Dh(≤h O), the hyperarithmetic degrees below Kleene's O, in the language of uppersemilattices with least and greatest element. This requires a new kind of initial-segment result and a new extension of embeddings result both in the hyperarithmetic setting.
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