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| Main Author: | |
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| Format: | Preprint |
| Published: |
2001
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0104025 |
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| _version_ | 1866910274014937088 |
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| author | Ferreira, Jailton C. |
| author_facet | Ferreira, Jailton C. |
| contents | The proof of Goedel's first incompleteness theorem includes the construction of an arithmetic formula G that represents the metamathematical statement: the formula G is not provable. This article examines the formula G (of Goedel). We demonstrated that there is no Goedel's number for the formula G if number of provable well formed formulae with one free variable is finite. If there is a non-finite number of provable propositions in the theory, then Goedel's formula also does not possess the Goedel's number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0104025 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | On the Goedel's formula Ferreira, Jailton C. General Mathematics The proof of Goedel's first incompleteness theorem includes the construction of an arithmetic formula G that represents the metamathematical statement: the formula G is not provable. This article examines the formula G (of Goedel). We demonstrated that there is no Goedel's number for the formula G if number of provable well formed formulae with one free variable is finite. If there is a non-finite number of provable propositions in the theory, then Goedel's formula also does not possess the Goedel's number. |
| title | On the Goedel's formula |
| topic | General Mathematics |
| url | https://arxiv.org/abs/math/0104025 |