Substructural fixedpoint theorems and the diagonal argument: theme and variations
Abstract
This article reexamines Lawvere's abstract, categorytheoretic proof of the fixedpoint theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixedpoint theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.00239
 Bibcode:
 2021arXiv211000239R
 Keywords:

 Mathematics  Category Theory;
 Computer Science  Logic in Computer Science;
 Mathematics  Logic;
 03B47;
 18A15;
 F.4.1
 EPrint:
 v1 20 pages