The present work determines the arithmetic complexity of the index sets of u.c.e. families which are learnable according to various criteria of algorithmic learning. Specifically, we prove that the index set of codes for families that are TxtFex\(^a_b\)-learnable is \(\Sigma _4^0\)-complete and that the index set of TxtFex\(^*_*\)-learnable and the index set of TxtFext\(^*_*\)-learnable families are both \(\Sigma _5^0\)-complete.

中文翻译：

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算术等级制中的学习理论II

本工作确定了可根据算法学习的各种标准学习的uce系列索引集的算术复杂度。具体来说，我们证明TxtFex \（^ a_b \）- learnable的族的索引集是\（\ Sigma _4 ^ 0 \） -complete，并且TxtFex \（^ * _ * \）的索引集-learnable和TxtFext \（^ * _ * \）- learnable族的索引集都是\（\ Sigma _5 ^ 0 \）- complete。