Substructural fixed-point theorems and the diagonal argument: theme and
variationsArticle
Authors: David Michael Roberts 1
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David Michael Roberts
1 School of Computer and Mathematical Sciences, The University of Adelaide, Adelaide, Australia
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.
Mark van Atten, Logic, epistemology, and the unity of science, Natural Constructive Proofs of $$A$$ via $$A \rightarrow B$$, Proof Paradoxes, and Impredicativity, pp. 417-498, 2024, 10.1007/978-3-031-52411-0_20.