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

compositionality:13527 - Compositionality, August 10, 2023, Volume 5 (2023) - https://doi.org/10.32408/compositionality-5-8
Substructural fixed-point theorems and the diagonal argument: theme and variationsArticle

Authors: David Michael Roberts 1

  • 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.

https://doi.org/10.32408/compositionality-5-8
Source: arXiv.org:2110.00239
Volume: Volume 5 (2023)
Published on: August 10, 2023
Imported on: May 2, 2024
Keywords: Mathematics - Category Theory,Computer Science - Logic in Computer Science,Mathematics - Logic,03B47, 18A15,F.4.1
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Discovery Projects - Grant ID: DP180100383; Funder: Australian Research Council (ARC); Code: DP180100383

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