Coinductive well-foundedness
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909669652430848 |
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| author | Petrakis, Iosif |
| author_facet | Petrakis, Iosif |
| contents | We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented subset of N has a least element if and only if it is downset located. The use of complemented subsets of N in the formulation of CLNP, instead of subsets of N, allows a positive approach to the subject that avoids negation. Generalising the coinductive well-foundedness of N, we define $\exists$-well-founded sets and we prove their fundamental properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coinductive well-foundedness Petrakis, Iosif Logic We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented subset of N has a least element if and only if it is downset located. The use of complemented subsets of N in the formulation of CLNP, instead of subsets of N, allows a positive approach to the subject that avoids negation. Generalising the coinductive well-foundedness of N, we define $\exists$-well-founded sets and we prove their fundamental properties. |
| title | Coinductive well-foundedness |
| topic | Logic |
| url | https://arxiv.org/abs/2506.16433 |