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On Rosser theories.

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Title: On Rosser theories.
Authors: Cheng, Yong1 (AUTHOR)
Source: Journal of Logic & Computation. Jul2025, Vol. 35 Issue 5, p1-28. 28p.
Subjects: Mathematical logic, Recursion theory, Generalization, Theorists
Abstract: Rosser theories play an important role in the study of the incompleteness phenomenon and meta-mathematics of arithmetic. In this paper, we first define the notions of |$n$| -Rosser theories, exact |$n$| -Rosser theories, effectively |$n$| -Rosser theories and effectively exact |$n$| -Rosser theories (see Definition 1.6). Our definitions are not restricted to arithmetic languages. Then we systematically examine properties of |$n$| -Rosser theories and relationships among them. Especially, we generalize some important theorems about Rosser theories for recursively enumerable sets in the literature to |$n$| -Rosser theories in a general setting. [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: On Rosser theories.
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  Data: <searchLink fieldCode="AR" term="%22Cheng%2C+Yong%22">Cheng, Yong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: Rosser theories play an important role in the study of the incompleteness phenomenon and meta-mathematics of arithmetic. In this paper, we first define the notions of |$n$| -Rosser theories, exact |$n$| -Rosser theories, effectively |$n$| -Rosser theories and effectively exact |$n$| -Rosser theories (see Definition 1.6). Our definitions are not restricted to arithmetic languages. Then we systematically examine properties of |$n$| -Rosser theories and relationships among them. Especially, we generalize some important theorems about Rosser theories for recursively enumerable sets in the literature to |$n$| -Rosser theories in a general setting. [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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    Identifiers:
      – Type: doi
        Value: 10.1093/logcom/exae085
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      – Code: eng
        Text: English
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        PageCount: 28
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      – SubjectFull: Mathematical logic
        Type: general
      – SubjectFull: Recursion theory
        Type: general
      – SubjectFull: Generalization
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      – TitleFull: On Rosser theories.
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              M: 07
              Text: Jul2025
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              Y: 2025
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