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Substructural fixed-point theorems and the diagonal argument: theme and variations (2110.00239v3)
Published 1 Oct 2021 in math.CT, cs.LO, and math.LO
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.