Abstract

The paper studies Rogers semilattices, i.e. upper semilattices induced by the reducibility between numberings. Under the assumption of Projective Determinacy, we prove that for every non-zero natural number \(n\), there are infinitely many pairwise elementarily non-equivalent Rogers semilattices for \(\Sigma^{1}_{n}\)-computable families.

中文翻译：

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解析编号的罗杰斯半格理论

摘要

该论文研究了罗杰斯半格，即由编号之间的可约性引起的上半格。在投影确定性的假设下，我们证明对于每个非零自然数\(n\)，对于\(\Sigma^{1}_{n}\)有无穷多个成对基本不等价的 Rogers 半格-可计算的家庭。