Substructural fixed-point theorems and the diagonal argument: theme and variations

David Michael Roberts

doi:10.32408/compositionality-5-8

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arXiv · 2110.00239

Substructural fixed-point theorems and the diagonal argument: theme and variations

David Michael Roberts

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Abstract

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.

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BibTeX RIS

David Michael Roberts. 2021-10-01. Substructural fixed-point theorems and the diagonal argument: theme and variations. https://doi.org/10.32408/compositionality-5-8

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