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

2023/08/10 by David Roberts · 4 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Argument (complex analysis) #Axiom #Diagonal #Discrete mathematics #Fixed point #Fixed-point theorem #Geometry #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematical analysis #Mathematical economics #Mathematics #Pure mathematics

paper · pdf · doi:10.32408/compositionality-5-8

published in Compositionality 5, 8

openalex created_date 2021/10/11 · openalex publication_date 2023/08/10 · rss pubdate 2023/08/10 · openalex updated_date 2026/08/05

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.

Citations

• Physics, Topology, Logic and Computation: A Rosetta Stone

Cited by

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