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Learning theory in the arithmetic hierarchy II

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Abstract

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.

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Acknowledgements

The authors would like to thank the anonymous referee for dilligent readings of the paper and thoughtful comments.

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Correspondence to Achilles A. Beros.

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Beros, A.A., Beros, K.A., Flores, D. et al. Learning theory in the arithmetic hierarchy II. Arch. Math. Logic 60, 301–315 (2021). https://doi.org/10.1007/s00153-020-00745-4

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  • DOI: https://doi.org/10.1007/s00153-020-00745-4

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