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Undecidability of the degree structure of primitive recursive m-reducibility.

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Title: Undecidability of the degree structure of primitive recursive m-reducibility.
Authors: Kalmurzayev, Birzhan S1 (AUTHOR), Bazhenov, Nikolay A1,2 (AUTHOR), Iskakov, Alibek M1 (AUTHOR)
Source: Journal of Logic & Computation. Jun2025, Vol. 35 Issue 4, p1-14. 14p.
Subjects: Recursive functions
Abstract: Let |$\mathbf{C}^{pr}_{m}$| be the upper semilattice of degrees of computable sets with respect to primitive recursive |$m$| -reducibility. We prove that the first-order theory of |$\mathbf{C}^{pr}_{m}$| is hereditarily undecidable. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Undecidability of the degree structure of primitive recursive m-reducibility.
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  Data: <searchLink fieldCode="AR" term="%22Kalmurzayev%2C+Birzhan+S%22">Kalmurzayev, Birzhan S</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Bazhenov%2C+Nikolay+A%22">Bazhenov, Nikolay A</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Iskakov%2C+Alibek+M%22">Iskakov, Alibek M</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: Let |$\mathbf{C}^{pr}_{m}$| be the upper semilattice of degrees of computable sets with respect to primitive recursive |$m$| -reducibility. We prove that the first-order theory of |$\mathbf{C}^{pr}_{m}$| is hereditarily undecidable. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1093/logcom/exae074
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        Text: English
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              Text: Jun2025
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