arXiv Open Access 2017

The $Σ_2$ theory of $\mathscr{D}_h(\leq_h \mathcal{O})$ as an uppersemilattice with least and greatest element is decidable

James Barnes

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Abstrak

We establish the decidability of the $Σ_2$ 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.

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math.LO

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James Barnes

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Barnes, J. (2017). The $Σ_2$ theory of $\mathscr{D}_h(\leq_h \mathcal{O})$ as an uppersemilattice with least and greatest element is decidable. https://arxiv.org/abs/1704.06347

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓