On Rosser theories
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914068596523008 |
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| author | Cheng, Yong |
| author_facet | Cheng, Yong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Rosser theories Cheng, Yong Logic 03F40, 03F30, 03F25 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. |
| title | On Rosser theories |
| topic | Logic 03F40, 03F30, 03F25 |
| url | https://arxiv.org/abs/2401.11749 |