Substructural fixed-point theorems and the diagonal argument: theme and variations
Category Theory
2024-08-07 v3 Logic in Computer Science
Logic
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.
Cite
@article{arxiv.2110.00239,
title = {Substructural fixed-point theorems and the diagonal argument: theme and variations},
author = {David Michael Roberts},
journal= {arXiv preprint arXiv:2110.00239},
year = {2024}
}
Comments
v1 20 pages; v2 22 pages, added additional final section on fixed-point operators; v3 final journal version