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The $\Sigma_2$ theory of $\mathscr{D}_h(\leq_h \mathcal{O})$ as an uppersemilattice with least and greatest element is decidable. (arXiv:1704.06347v1 [math.LO])
来源于:arXiv
We establish the decidability of the $\Sigma_2$ theory of
$\mathscr{D}_h(\leq_h \mathcal{O})$, the hyperarithmetic degrees below Kleene's
$\mathcal{O}$, 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. 查看全文>>
