Substructural fixed-point theorems and the diagonal argument: theme and variations
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913458855870464 |
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| author | Roberts, David Michael |
| author_facet | Roberts, David Michael |
| contents | This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_00239 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Substructural fixed-point theorems and the diagonal argument: theme and variations Roberts, David Michael Category Theory Logic in Computer Science Logic 03B47, 18A15 F.4.1 This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange. |
| title | Substructural fixed-point theorems and the diagonal argument: theme and variations |
| topic | Category Theory Logic in Computer Science Logic 03B47, 18A15 F.4.1 |
| url | https://arxiv.org/abs/2110.00239 |