Substructural fixed-point theorems and the diagonal argument: theme and variations
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.00239
- arXiv:
- arXiv:2110.00239
- Bibcode:
- 2021arXiv211000239R
- Keywords:
-
- Mathematics - Category Theory;
- Computer Science - Logic in Computer Science;
- Mathematics - Logic;
- 03B47;
- 18A15;
- F.4.1
- E-Print:
- v1 20 pages