On Rosser theories.
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| Title: | On Rosser theories. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 0955792X |
| DOI: | 10.1093/logcom/exae085 |
