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

DOI10.32408/COMPOSITIONALITY-5-8arXiv2110.00239OpenAlexW3202332511WikidataQ122196025 ScholiaQ122196025MaRDI QIDQ6050008

David Michael Roberts

Publication date: 11 October 2023

Published in: Compositionality (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2110.00239

zbMATH Keywords

substructural logicfixed-point theoremdiagonal argument

Mathematics Subject Classification ID

Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Proof-theoretic aspects of linear logic and other substructural logics (03F52) Categories and theories (18C99)

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